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- [[Category:signal]] Compute the power and energy of the signal1,007 B (151 words) - 13:45, 24 February 2015
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- == Signal ==917 B (143 words) - 09:29, 4 September 2008
- == Signal Energy == == Signal Power ==650 B (86 words) - 06:49, 3 September 2008
- The function that we are using in this example to compute the signal power and energy is:1 KB (170 words) - 18:37, 3 September 2008
- ...e Signal <math>x(t)=3sin(2*pi*3t)</math>, Find the energy and power of the signal from 0 to 5 seconds.1 KB (206 words) - 08:36, 4 September 2008
- This page calculates the Energy and Power of the signal <math>2\sin(t)\cos(t)</math>1 KB (221 words) - 08:17, 4 September 2008
- == Signal Energy == The signal energy expanded from <math>t_1\!</math> to <math>t_2\!</math> is defined as1 KB (172 words) - 13:29, 4 September 2008
- == Signal Energy and Power Calculations == The energy of a signal within specific time limits is defined as:655 B (97 words) - 15:50, 4 September 2008
- Power of the equation <math>e^{-2t}u(t)</math> is 0 because the energy of the signal is < ∞329 B (60 words) - 14:39, 4 September 2008
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668 B (104 words) - 15:05, 4 September 2008
- == Energy of a Signal== == Power of a Signal ==536 B (79 words) - 15:09, 4 September 2008
- [[Category:signal]] Given complex signal <math>f(t) = \cos(t) + j \sin(t)</math>, find <math>E_\infty</math> and <ma4 KB (734 words) - 15:54, 25 February 2015
- For a continuous-time signal <br> ...m_{T \to \infty} {\frac{E(\infty)}{2T}} = 0 ................ Finite-energy Signal</math><br>647 B (89 words) - 21:00, 4 September 2008
- Computation of Signal Energy and power. Source for definition Of Continuous Signal: Wikipedia.778 B (99 words) - 13:21, 5 September 2008
- == Signal ==1 KB (189 words) - 21:40, 4 September 2008
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1 KB (169 words) - 18:20, 5 November 2010
- The formula for the energy of this signal is given by: The power of this signal is 0 because the energy of the signal is not <math>\infty</math>267 B (48 words) - 07:53, 5 September 2008
- Consider the signal747 B (114 words) - 14:19, 5 September 2008
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740 B (105 words) - 18:58, 5 September 2008
- The energy of a signal can by computed by the following Energy formula: on the other hand, power of a signal can be calculated by:574 B (92 words) - 18:37, 5 September 2008
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- '''Question:''' Compute the Fourier transform of the signal x(t) equal to: The Fourier Transform of a signal in Continuous Time is defined by:1 KB (188 words) - 11:09, 17 October 2008
- As seen below in the picture, a ct signal is converted to DT and then recovered using zero order interpolation.<br>409 B (76 words) - 13:12, 10 November 2008
- * [[CS-2: Signal Processing_Old Kiwi]]202 B (25 words) - 20:04, 9 March 2008
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- =GPS Signal Processing= ...iving further research and development. This research has led to improved signal processing and has led to the use of the Fast Fourier Transform.1 KB (248 words) - 11:07, 22 September 2009
- ...It is band-limited. This means that the Fourier transform of the original signal, also known as the spectrum, is 0 for |f| > B, where B is the bandwidth. ...l to the sampling period T, <math>{H_r}(f)</math>, to isolate the original signal.2 KB (436 words) - 19:51, 22 September 2009
- ==Audio Signal Filtering== ...ed to an electrical signal by a transducer, which then relays the "analog" signal to an A/D converter.5 KB (822 words) - 11:54, 21 September 2012
- [[Category:signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''1 KB (184 words) - 19:33, 16 March 2015
- [[Category:signal]] keywords:signal energy, exercises1 KB (207 words) - 16:04, 25 February 2015
- [[Category:signal]] =Continuous-Time (Average) Signal Power=1 KB (220 words) - 10:49, 21 April 2015
- [[Category:signal]] [[Category:continuous-time signal]]4 KB (595 words) - 11:01, 21 April 2015
- Topic: Signal Energy and Power ...</math> and the power <math>P_\infty</math> of the following discrete-time signal2 KB (317 words) - 16:18, 26 November 2013
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- = [[:Category:Problem_solving|Practice Question]] on the Nyquist rate of a signal = Is the following signal band-limited? (Answer yes/no and justify your answer.)4 KB (666 words) - 10:29, 11 November 2011
- = [[:Category:Problem_solving|Practice Question]] on signal modulation = Let x(t) be a signal whose Fourier transform <math>{\mathcal X} (\omega) </math> satisfies2 KB (393 words) - 10:31, 11 November 2011
- = [[:Category:Problem_solving|Practice Question]] on signal modulation = Let x(t) be a signal whose Fourier transform <math>{\mathcal X} (\omega) </math> satisfies2 KB (400 words) - 10:31, 11 November 2011
- = Audio Signal Generating and Processing Project = :::In this case, the signal is preserved, but at a lower sampling frequency. If play at the original fr5 KB (820 words) - 07:19, 21 March 2013
- = Audio Signal Processing with Down-sampler and LPF Investigate = ...o song. The effect of the LPF is less noticeable compared with human voice signal.10 KB (1,707 words) - 10:44, 6 May 2012
- [[Category:Digital Signal Processing]] ...://www.projectrhea.org/learning/practice.php Practice Problems] on Digital Signal Processing6 KB (801 words) - 22:04, 19 April 2015
- [[Category:Audio Signal Generating and Processing Project]] =Audio Signal Generating and Processing Project, Previous method=6 KB (931 words) - 20:33, 15 November 2011
- #REDIRECT [[ECE438 digital signal processing course motivations]]65 B (7 words) - 06:25, 28 October 2013
- =Lab Wiki: [[2013_Fall_ECE_438_Boutin|ECE 438: Digital Signal Processing With Applications]], Fall 2013=2 KB (341 words) - 15:54, 14 August 2013
- [[Category:digital signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''2 KB (319 words) - 10:50, 27 September 2013
- [[Category:signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''2 KB (189 words) - 08:26, 11 November 2013
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- [[Category:signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''1 KB (134 words) - 09:12, 19 August 2019
- [[Category:signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''6 KB (759 words) - 08:10, 11 November 2013
- [[Category:signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''1,002 B (119 words) - 05:58, 28 October 2013
- [[Category:signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''4 KB (471 words) - 19:34, 9 February 2015
- [[Category:signal processing]]706 B (95 words) - 11:20, 14 October 2014
- '''The [http://mireilleboutin.com Boutin] Lectures on Digital Signal Processing - Part 1''' ...cy domain view of the relationship between a signal and a sampling of that signal. ==3 KB (409 words) - 15:48, 24 March 2015
- [[Category:signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''3 KB (389 words) - 19:26, 16 March 2015
- ...015_Fall_ECE_438_Boutin_Digital Signal Processing With Application|Digital Signal Processing With Application]] ...015_Fall_ECE_438_Boutin_Digital Signal Processing With Application|Digital Signal Processing With Application]]. Please leave me a comment below if you have914 B (125 words) - 03:39, 29 November 2015
- <center><font size= 4>Digital Signal Processing With Application</font size> ...value) of two different transmitted frequencies component in the received signal.3 KB (417 words) - 04:38, 29 November 2015
- [[Category:signal]] [[Category:continuous-time signal]]2 KB (373 words) - 10:09, 22 January 2018
- [[Category:signal]] [[Category:continuous-time signal]]2 KB (229 words) - 10:22, 22 January 2018
- Topic: Signal Energy and Power ...</math> and the power <math>P_\infty</math> of the following discrete-time signal2 KB (263 words) - 11:13, 22 January 2018
- ...nfty</math> and the power <math class="inline">P_\infty</math> of this DT signal: Norm of a signal:1 KB (196 words) - 19:39, 1 December 2018
- Compute the energy and the power of the CT sinusoidal signal below:1 KB (178 words) - 19:48, 1 December 2018
Page text matches
- :[[ECE438|ECE438: "Digital Signal Processing with Applications"]]2 KB (209 words) - 13:07, 9 September 2022
- ...n evaluating the Region of Convergence (ROC) of the Laplace transform, the signal has a Fourier transform if:2 KB (268 words) - 12:14, 10 December 2008
- *[[ECE438|ECE438: "Digital Signal Processing with Applications]], the main page for this popular senior level ...tal_signal_processing_practice_problems_list|Practice problems on "Digital Signal Processing"]]6 KB (877 words) - 07:22, 21 March 2013
- ##[[Signal Energy and Power_(ECE301Summer2008asan)|Signal Energy and Power]] ...CT signal by its samples:_(ECE301Summer2008asan)| Representation of a CT signal by its samples]]7 KB (921 words) - 06:08, 21 October 2011
- The sampling theorem states that for a signal x(t) to be uniquely reconstructed, its X(jw) = 0 when |w| > wm, and the sam A signal can be recovered from sampling if4 KB (667 words) - 11:15, 21 November 2008
- Let x(t) be a BAND-LIMITED signal with X(w) = 0 for |w| > w_m.625 B (99 words) - 13:07, 8 November 2010
- ...--[[User:Asan|Asan]] 03:42, 14 June 2008 (EDT)(It is the system... not the signal)3 KB (534 words) - 11:16, 30 January 2011
- ...e. The transformation consists of a shift and time scaling. The resulting signal is shifted to the left by 5 and time scaled so the new times are divided by ...even and odd parts of a signal x[n]. x1[n] = (x[n] + x[-n])/2 is the even signal. It can be found by plotting x[n]/2 and x[-n]/2 then summing the two signa877 B (156 words) - 10:58, 21 November 2008
- (a) Derive the condition for which the discrete time complex exponetial signal x[n] is periodic.2 KB (270 words) - 10:59, 21 November 2008
- The unit impulse response of an LTI system is the CT signal1 KB (227 words) - 10:55, 30 January 2011
- The unit impulse response of an LTI system is the CT signal1 KB (222 words) - 10:57, 30 January 2011
- The unit impulse response of an LTI system is the CT signal409 B (61 words) - 10:59, 30 January 2011
- (a) The FT of <math>X(j\omega)</math> of a continuous-time signal x(t) is periodic (b) The FT of <math>X(e^{j\omega})</math> of a continuous-time signal x[n] is periodic4 KB (777 words) - 11:49, 21 November 2008
- .../math> of the signal x[n] is also periodic with period N. For the periodic signal x[n], find the values of <math>a_0,a_1,...,a_{N-1}.</math> Express your an 1)b)Evaluate the value of <math>(1/N)*\sum_{n=<N>}|x[n]|^2</math> for the signal x[n] given in part (a).4 KB (815 words) - 10:57, 21 November 2008
- [[Category:signal processing]] =Signal Sampling=1 KB (176 words) - 07:04, 16 September 2013
- *[[HKNQE_Communications_and_Signal_Processing|Communications and Signal Processing]]626 B (74 words) - 09:44, 3 December 2008
- = Communication, Networking, Image and Signal Processing (CNSIP) Research in ([[ECE]])= Purdue University has a rich and long history in communications and signal processing. For example, did you know the the following facts?3 KB (360 words) - 07:01, 25 June 2012
- :"A Signal-Processing Approach to Modeling Vision, and Applications" ...these results to image compression and quality assessment, as well as some signal processing problems (and their solutions) that emerged in applying the psyc5 KB (656 words) - 14:36, 4 May 2011
- <b>Periodic CT Signal:</b> ...es of t. The fundamental period is the smallest period of all periods of a signal (denoted by <math> T_0\ </math>).1 KB (206 words) - 16:58, 23 April 2013
- ...shift in the input signal results in an identical time shift in the output signal.4 KB (748 words) - 17:24, 23 April 2013
- ...ignal would, and writing all the transforms or "things" that happen to the signal using different variables, then we go back and substitute so it all works o3 KB (486 words) - 11:10, 8 December 2008
- A band-limited signal can be recovered by sampling if the sampling frequency <math> \omega_s </ma589 B (78 words) - 13:08, 8 December 2008
- This is an example of convolution done two ways on a fairly simple general signal.3 KB (549 words) - 10:37, 30 January 2011
- The command is ifft. It takes in a vector representing your signal and produces a vector of the fourier series coefficients. Two examples are The signal is represented by the graph below and is periodic for all time:5 KB (834 words) - 17:26, 23 April 2013
- and let <math> x(t)\ </math> denote the signal obtained by using <math> X(j\omega)\ </math> in the right hand side of Equa1 KB (227 words) - 11:54, 10 December 2008
- ...an then apply the 'effect' of the system to each individual impulse of the signal, sum them, and find the resulting output.2 KB (322 words) - 17:27, 23 April 2013
- ...hey are for periodic signals also. The formula for transforming a periodic signal is (I believe) the first one on the table. :: Fourier Transform is for all signal. It represents signals as an integral of complex exponentials.1 KB (186 words) - 17:25, 23 April 2013
- ...he Fourier Transform.... In particular, Fourier reasoned that an aperiodic signal can be viewed as a periodic singal with an infinite period." An example of ...nd the sound of the musical chord represented by these notes (the function/signal itself).3 KB (431 words) - 17:29, 23 April 2013
- ...sion for CT signals, and performing a summation for each dimension in a DT signal.2 KB (303 words) - 10:13, 12 December 2008
- ...pled signal that is band limited to about 20kHz, then we should sample the signal at twice that frequency.925 B (151 words) - 17:28, 23 April 2013
- The sampling theorem tells us that we can perfectly reconstruct a signal if the following two conditions are observed: # The signal has a finite bandwidth B. (meaning the signal is band limited)3 KB (591 words) - 17:24, 23 April 2013
- ...sampled greater than the Nyquist Rate in order to reconstruct the original signal. The effect of undersampling, or sampling at a rate below that of the Nyqui ...ponds to a frequency of .2 rev/sec. This frequency is the frequency of the signal. The small red dot is just an indicator on a part of the wheel to make it e3 KB (446 words) - 06:21, 18 September 2013
- ...ecause it does not specify from what the signal is being recreated. If the signal is for example not band-limited, it cannot be reconstructed at all. ...an the Nyquist rate in rare cases you are able to properly reconstruct the signal.4 KB (689 words) - 12:48, 12 December 2008
- Let <math> x(t)\ </math> be a BAND-LIMITED signal with <math> X(\omega) = 0\ </math> for <math> |\omega| > \omega_m\ </math>.739 B (108 words) - 12:43, 18 December 2008
- : <code>Plot(Y)</code> Plots vector Y (useful to visualize an audio signal). Plotting at different frequencies: ...ode>x=y ( 1 : N : length(y) );</code> will create a vector x, which is the signal Y at 1/N of its original frequency. (takes every N element of y and puts in725 B (116 words) - 13:10, 18 December 2008
- *[[ECE:CNSIP area| Communication, Networking, Signal and Image Processing (CNSIP) area (from ECE)]]493 B (74 words) - 11:24, 25 May 2009
- :[[2015_Spring_ECE_438_Ersoy|ECE438: "Digital SIgnal Processing", Prof. Ersoy]] :[[2014_Fall_ECE_438_Boutin|ECE438: "Digital SIgnal Processing"]]13 KB (1,570 words) - 13:53, 7 August 2018
- =ECE 438: Digital Signal Processing with Applications=558 B (80 words) - 09:55, 27 February 2009
- | align="right" style="padding-right: 1em;" | Wednesday || 01/14/09 || Signal types, characteristics, transformations || 1.1.1-1.1.3 || CT and DT signals6 KB (689 words) - 07:59, 2 August 2010
- *[[lecture1_ECE301Fall2008mboutin|Lecture 1]]: Intro; Example of DT signal (text) and system (enigma machine). *[[Lecture2_ECE301Fall2008mboutin|Lecture 2]]: Example of CT signal (sound); Creating sounds in Matlab; Example of linear system.5 KB (720 words) - 06:10, 16 September 2013
- I am trying to figure out how to compute the norm of the DT signal2 KB (396 words) - 16:53, 23 April 2013
- * A typical plan of study for a first semester Signal Processing Grad Student (MS or PhD) is: ECE600, ECE538, MA511 ==If you are a direct PhD student interested in the signal processing area==2 KB (308 words) - 13:06, 30 September 2009
- [[Category:signal processing]]865 B (78 words) - 06:37, 16 September 2013
- [[Category:signal processing]] 2) Digital Signal = a signal that can be represented by a sequence of 0's and 1's.3 KB (532 words) - 06:43, 16 September 2013
- *<math>\omega_m</math>: Maximum frequency in a band-limited signal (<math> = max(\{|w|\ :\ w \neq 0\})</math> ...hen the band-limited signal can be uniquely reconstructed from the sampled signal.2 KB (406 words) - 11:08, 12 November 2010
- [[Category:signal processing]] <li>Signal Characteristics</li>3 KB (508 words) - 06:43, 16 September 2013
- [[Category:signal processing]] <p>Comb operator multiplies a signal by an "impulse train".2 KB (408 words) - 06:43, 16 September 2013
- [[Category:signal processing]]2 KB (359 words) - 06:43, 16 September 2013
- *[[CT Time-averaged Power of a Signal over an infinite interval_ECE301Fall2008mboutin]] {{:CT Power of a Signal_8 KB (989 words) - 07:20, 5 February 2009
- ...is is an advanced capture, process and display technology which enables RF signal analysis never before possible. Featured capabilities, discussed and demons *Automatic RF signal identification967 B (123 words) - 12:47, 5 February 2009
- ...Fourier transform of x[n], which is the sampled signal of continuous time signal x(t) <br>546 B (93 words) - 20:27, 18 February 2009
- [[Category:signal processing]]769 B (105 words) - 06:44, 16 September 2013
- ...ng: when you upsample after having downsampled, you introduce zeros in the signal that were not previously there. To undo a downsampling, you have to use an2 KB (383 words) - 21:03, 10 February 2009
- ...at starts at -1e-4 and goes to 1e-4. The ideal sampler creates a discrete signal with 5 points each 5e-5 apart.844 B (152 words) - 18:26, 11 February 2009
- ...e relationship between the FT of a signal and the FT of a sampling of that signal. Anybdy sees a mistake? Perhaps one can rewrite this so it becomes a bit cl2 KB (374 words) - 12:35, 17 February 2009
- *Basic properties of signal and systems <li>Don't forget the different signal's metrics! --[[User:Mboutin|Mboutin]] 16:15, 17 February 2009 (UTC)</li>710 B (115 words) - 14:35, 17 February 2009
- [[Category:signal processing]] <p>use DFT to approximate <math>X(a)</math> for a DT signal x(n)2 KB (376 words) - 06:44, 16 September 2013
- ...o union between the ROCs, then it's null such that there is no ROC for the signal --[[User:Mlo|Mlo]] 15:18, 24 February 2009 (UTC)549 B (90 words) - 08:37, 26 February 2009
- ...rect in time. In frequency, this is multiplication of the spectrum of the signal with the spectrum of the rect (which is a sinc). This is effectively a coa906 B (143 words) - 12:40, 4 March 2009
- [[Category:signal processing]]3 KB (522 words) - 06:45, 16 September 2013
- ** Signal Processing258 B (29 words) - 08:56, 27 March 2009
- [[Category:signal processing]]2 KB (324 words) - 06:45, 16 September 2013
- Note: PM refers to the official course book, Digital Signal Processing, 3rd edition, J.G. Proakis and D.G. Manolakis. ...due.edu/~bouman/ece438/lecture/module_1/1.1_signals/1.1.1_signal_types.pdf Signal Types]8 KB (1,226 words) - 11:40, 1 May 2009
- :[[ECE438|ECE438: "Digital Signal Processing with Applications"]] *[[ECE438|ECE 438]]: "Digital Signal Processing with Applications"4 KB (474 words) - 07:08, 4 November 2013
- =Rhea Section for [[ECE438|ECE 438: Digital Signal Processing with Applications]] Professor [[User:mboutin|Boutin]], Fall 20097 KB (1,067 words) - 12:05, 25 June 2010
- * [[HW1.5 Nicholas Browdues - Signal Power and Energy_ECE301Fall2008mboutin]] * [[HW1.5 Ben Laskowski - Signal Power and Energy_ECE301Fall2008mboutin]]24 KB (3,272 words) - 06:58, 1 September 2010
- == Continuous Signal == Continuous signal is a signal that varies with time, and can be represented as a function of time, x(t).2 KB (311 words) - 16:27, 3 December 2008
- %as we replace t with 2t,so double the time in signal function %which also means double the frequency of each signal2 KB (347 words) - 17:52, 3 September 2008
- jpbak=flipud(jp); %reverse the signal544 B (83 words) - 18:34, 1 September 2008
- [[Category:signal]] Compute the power and energy of the signal1,007 B (151 words) - 13:45, 24 February 2015
- == Periodic Signal == Notice, the signal is the same throughout each cycle.481 B (60 words) - 07:15, 14 April 2010
- == Signal ==917 B (143 words) - 09:29, 4 September 2008
- == Signal ==1 KB (193 words) - 13:29, 2 September 2008
- - Signal Processing952 B (163 words) - 13:23, 4 September 2008
- == Signal ==945 B (160 words) - 16:01, 3 September 2008
- Example of Periodic Function since it is a repeated signal every cycle --> Triangle Wave1 KB (171 words) - 06:06, 29 August 2011
- == Signal Energy == == Signal Power ==650 B (86 words) - 06:49, 3 September 2008
- The signal is: x(t) = 2cos(2t)644 B (94 words) - 06:39, 3 September 2008
- The function that we are using in this example to compute the signal power and energy is:1 KB (170 words) - 18:37, 3 September 2008
- ...e Signal <math>x(t)=3sin(2*pi*3t)</math>, Find the energy and power of the signal from 0 to 5 seconds.1 KB (206 words) - 08:36, 4 September 2008
- This page calculates the energy and power of the <math>2\sin(t)\cos(t)</math> signal.1 KB (240 words) - 08:03, 4 September 2008
- A discrete time signal is periodic if there exists T > 0 such that x(t + T) = x(t) A continuous time signal is periodic if there exists some integer N > 0 such that x[n + N] = x[n]1 KB (205 words) - 07:20, 14 April 2010
- This page calculates the Energy and Power of the signal <math>2\sin(t)\cos(t)</math>1 KB (221 words) - 08:17, 4 September 2008
- A continuous time signal is periodic if there exists a value <math> T </math> such that <math> x(t + A discrete time signal is periodic if there exists a value <math> N </math> such that <math> X[n +1 KB (169 words) - 07:22, 14 April 2010
- Let us find the energy and average power of a signal <math>x(t) = 5e^{5t}</math> for the time interval [0,5]739 B (117 words) - 10:12, 4 September 2008
- The following is the energy expended by the signal <math> sin(2t) </math> from <math> t = 0 </math> to <math> t = 4\pi </math> The following is the average power expended by the signal <math> sin(2t) </math> from <math> t = 0 </math> to <math> t = 4\pi </math>897 B (142 words) - 10:00, 4 September 2008
- signal = sin(2*pi * t * NV(i)); sound(signal, 1/delta);1 KB (160 words) - 15:33, 4 September 2008
- == Signal ==888 B (154 words) - 10:47, 4 September 2008
- == Signal ==888 B (154 words) - 10:48, 4 September 2008
- ==Periodic Signal== In discrete time, a signal x[n] is considered a '''periodic signal''' if there exists a natural number N such that for all integers n, x[n+N]2 KB (279 words) - 07:18, 14 April 2010
- %c) Play signal corresponding to the tune of a) and rescale2 KB (329 words) - 14:14, 4 September 2008
- %Take the signal and transform it to y(t)=wave(2t)3 KB (496 words) - 12:53, 4 September 2008
- == Signal Energy == The signal energy expanded from <math>t_1\!</math> to <math>t_2\!</math> is defined as1 KB (172 words) - 13:29, 4 September 2008
- %Changin signal to x[-0.5n]:511 B (91 words) - 16:01, 5 September 2008
- == Signal Energy and Power Calculations == The energy of a signal within specific time limits is defined as:655 B (97 words) - 15:50, 4 September 2008
- == Signal == The signal used was <math>cos(3t)</math>.569 B (88 words) - 13:55, 4 September 2008
- <math>x[n]=</math><math>j^{n}</math> is a discrete time (DT) periodic signal. It's period is 4*k, where k is an integer. However, it's fundamental perio <math>x[n]=\cos{n}</math> is an example of a non-periodoc signal because there is not integer value for n such that <math>x[n+N]=x[n]</math>883 B (143 words) - 07:24, 14 April 2010
- Compute the Energy and Power of the signal <math>x(t)=\dfrac{2t}{t^2+5}</math> between 3 and 5 seconds.966 B (143 words) - 14:42, 4 September 2008
- Power of the equation <math>e^{-2t}u(t)</math> is 0 because the energy of the signal is < ∞329 B (60 words) - 14:39, 4 September 2008
- == Energy of a Signal== == Power of a Signal ==536 B (79 words) - 15:09, 4 September 2008
- ==Signal Energy and Power== Define a signal (either CT or DT) and compute its energy and its power. Post your answer on2 KB (248 words) - 13:04, 5 September 2008
- A continuous time signal x(t) is periodic if there exists T such that x(t + T) = x(t) for all t. <br A discrete time signal x[n] is periodic if there exists some integer N such that x[n + N] = x[n] f1 KB (192 words) - 07:28, 14 April 2010
- Energy of a Signal: <math>E = {1\over(t2-t1)}\int_{t_1}^{t_2} \! |f(t)|^2 dt</math> Power of a Signal: <math>P = \int_{t_1}^{t_2} \! |f(t)|^2\ dt</math>896 B (142 words) - 16:54, 4 September 2008
- [[Category:signal]] Given complex signal <math>f(t) = \cos(t) + j \sin(t)</math>, find <math>E_\infty</math> and <ma4 KB (734 words) - 15:54, 25 February 2015
- Definiton: A DT signal x[n] is called periodic if there exists an integer N such that x[n+N]=x[n] Example: sin[n] is not a periodic DT signal because we need a value on N such that sin(n+N)=sin(n) for all n. Every pos835 B (141 words) - 07:26, 14 April 2010
- I will calculate the energy expended by the signal <math>sin(2t)</math> from <math> t = 0 </math> to <math> t = 8\pi </math> -819 B (140 words) - 17:25, 4 September 2008
- % data = digital signal, Fs = Frequency, nbits = number of bits per sample<br>2 KB (268 words) - 17:27, 4 September 2008
- A Continuous Time signal is said to be periodic if there exists <math>\ T > 0</math> such that <math A Discrete Time signal is said to be periodic if there exists <math>\ N > 0</math> (where N is an1 KB (221 words) - 12:21, 5 September 2008
- The definition of a periodic DT signal is that there exists an integer N such that <math>x[n+N] = x[n]</math> for On the other hand, <math>cos(n)</math> is not a periodic signal because there is no integer that is multple of <math>2\pi</math> and is an656 B (115 words) - 06:13, 5 September 2008
- Suppose a signal is defined by <math>cos(t)</math> Suppose we want to compute the energy of the signal <math>cos(t)</math> in the interval <math>0</math> to <math>2\pi</math>.1 KB (199 words) - 20:14, 4 September 2008
- == Periodic Signal Definition == *For a Continuous-time signal1 KB (209 words) - 09:49, 5 September 2008
- '''''I chose to compute the energy and power for the signal f(t) = 3x.'''''574 B (97 words) - 05:11, 5 September 2008
- For a continuous-time signal <br> ...m_{T \to \infty} {\frac{E(\infty)}{2T}} = 0 ................ Finite-energy Signal</math><br>647 B (89 words) - 21:00, 4 September 2008
- == Signal energy == == Signal power ==726 B (122 words) - 20:45, 4 September 2008
- This is a discrete signal too.677 B (97 words) - 20:44, 4 September 2008
- Computation of Signal Energy and power. Source for definition Of Continuous Signal: Wikipedia.778 B (99 words) - 13:21, 5 September 2008
- ...e'' function, this is not the case. The definition for a periodic discrete signal is that there exists an ''integer'' <math>N > 0</math> such that <math>x[n1 KB (189 words) - 21:21, 4 September 2008
- == Signal ==1 KB (189 words) - 21:40, 4 September 2008
- ...rst signal is a triangular wave which has period of 10 seconds. The second signal is a bunch of noises. title('Periodic Signal');656 B (87 words) - 21:36, 4 September 2008
- ==Signal==1 KB (204 words) - 22:14, 4 September 2008
- == Signal Energy == Signal Energy expended from <math>t_1\!</math> to <math>t_2\!</math> for CT functi2 KB (295 words) - 06:34, 5 September 2008
- == For a Continuous Time Signal==788 B (127 words) - 12:34, 5 September 2008
- A periodic signal is one that for a given real number "a": ===Periodic Signal===1 KB (195 words) - 07:20, 14 April 2010
- Compute the Energy and Power of the signal <math>x(t)=\dfrac{2t}{t^2+5}</math> between 0 and 2 seconds.811 B (121 words) - 07:08, 5 September 2008
- ==Energy of a CT signal== ==Power of a CT signal==324 B (62 words) - 07:39, 5 September 2008
- The formula for the energy of this signal is given by: The power of this signal is 0 because the energy of the signal is not <math>\infty</math>267 B (48 words) - 07:53, 5 September 2008
- == The following signals are shown to be either an energy signal or a power signal == A consequence of this is that P=0. If the energy of the signal was infinite, then the power would be536 B (94 words) - 08:24, 5 September 2008
- A DT signal x[n] is called periodic if there exists an integer N such that x[n+N] = x[n A CT signal x(t) is called periodic if there exists an integer T > 0 such that x(t+T) =831 B (141 words) - 08:17, 5 September 2008
- Example of a periodic signal fundamental period of signal N=4960 B (171 words) - 07:13, 14 April 2010
- A signal is periodic if there exists some T>0 such that: A signal is NOT periodic if the converse is true, there DOESN'T exists some T>0 such688 B (106 words) - 07:08, 14 April 2010
- == Signal Energy == find the signal energy of <math>x(t)=e^{4t}\!</math> on <math>[0,1]\!</math>700 B (110 words) - 08:53, 5 September 2008
- frequencies are the same, to produce a new signal. This is not true, however, for the case of multiplication. If640 B (98 words) - 08:50, 5 September 2008
- Given the Signal x(t) = 4sin(2 * pi * 6t), Find the energy and power of the signal from 2 to 6 seconds.1 KB (193 words) - 09:32, 5 September 2008
- In CT let x(t)=e^[1+j2)t]=(e^t)×[cos(2t)+ jsin(2t)] is a non-periodic signal because there is no T for which x(t+T)= x(t). In this case the signals amp563 B (104 words) - 09:23, 5 September 2008
- In Signals and Systems we will most commonly see complex numbers in signal analysis. Complex numbers are broken down into sin and cosine wave form and583 B (93 words) - 09:35, 5 September 2008
- ...are most frequently encountered in Electrical Engineering in the field of Signal Analysis. In this field complex numbers are broken down to terms of sine an614 B (98 words) - 09:41, 5 September 2008
- =Signal Power= =Signal Energy=722 B (108 words) - 10:47, 5 September 2008
- == Discrete time periodic signal Example == [[Image:dts_ECE301Fall2008mboutin.png|200px|thumb|left|Periodic Discrete Time Signal]]575 B (98 words) - 10:58, 5 September 2008
- % wavread command converts the .wav file to the digital signal data x[n] %wavplay command makes us listen to the digital signal x[n]1,015 B (164 words) - 14:14, 5 September 2008
- The energy and power of a signal can be found through the use of basic calculus. For the signal y(t) from 0 to 10 seconds, with y = <math>7x^3</math>552 B (84 words) - 12:42, 5 September 2008
- ==Periodic Signal== A continuous time (CT) signal is periodic if it there exists some T such that x(t+T)=x(t) for all t.811 B (148 words) - 13:12, 5 September 2008
- ==Periodic Signal== to prove a CT signal is continuous we must prove that there exists a value T such that x(t) = x(388 B (84 words) - 13:37, 5 September 2008
- An example of a complex signal/system would be '''x = 10 + 12j''' We can test to see if our function\signal is periodic by '''<math>{\omega/ 2\Pi = rational number!}</math>'''1 KB (189 words) - 14:17, 5 September 2008
- Suppose the signal to be <math>x(t)=cos(5t)</math>.682 B (110 words) - 13:42, 5 September 2008
- Consider the signal747 B (114 words) - 14:19, 5 September 2008
- %using the waveread command to convert the .wav file to the digital signal 'song' %using the waveplay command to listen the digital signal we have just converted at 44100 hz sampling rate1 KB (195 words) - 14:47, 5 September 2008
- % wavread command converts the .wav file to the digital signal data x[n] %digital signal x[n] can be heard because of the Waveplay command834 B (138 words) - 14:31, 5 September 2008
- The signal is f(t) = sin(t) and t1=0 and t2=2pi Therefore for our signal:1,005 B (178 words) - 14:45, 5 September 2008
- == Signal ==603 B (94 words) - 14:51, 5 September 2008
- ==Periodic Signal== Above is an example of a periodic signal: <math>y(t) = \sin(\pi t)</math>801 B (121 words) - 07:28, 14 April 2010
- ==Energy of a signal== Consider the signal <math>\ y = \sin(t)</math>841 B (130 words) - 15:58, 5 September 2008
- The energy expanded from a time t1 to a time t2 in a CT signal is calculated by1,016 B (167 words) - 15:48, 5 September 2008
- '''Non periodic signal''' is a signal that doesnt repeat its values after some definite period has been added to Example of a non periodic signal.2 KB (291 words) - 07:03, 14 April 2010
- %reverse the signal473 B (72 words) - 16:43, 5 September 2008
- YBACK=flipud(Y); %reverse the signal574 B (87 words) - 17:46, 5 September 2008
- ==Signal Energy and Power==339 B (38 words) - 18:19, 5 September 2008
- == Signal Energy == ==Signal Energy Example==601 B (94 words) - 18:35, 5 September 2008
- The energy of a signal can by computed by the following Energy formula: on the other hand, power of a signal can be calculated by:574 B (92 words) - 18:32, 5 September 2008
- Energy of a CT Signal Energy of a DT Signal232 B (39 words) - 19:00, 5 September 2008
- The energy of a signal can by computed by the following Energy formula: on the other hand, power of a signal can be calculated by:574 B (92 words) - 18:37, 5 September 2008
- Compute the energy and power of a CT signal <math>y=2e^t</math> from (0,10)596 B (90 words) - 18:57, 5 September 2008
- Time Invariant system is a system that doesn't depend on the time when a signal is inputed into the system. If the system is shifted after the signal undergoes the transformation, then <math>y_2(t) = y(t - \delta) = 2x(t - \d1 KB (255 words) - 07:26, 7 September 2008
- If the signal is shifted at the output, <math>Y[n] = Y_k[n - \alpha] = (k+1)^2\delta[n-(k ...al doesn't match, as the coeefeicent change according to the time when the signal is inputted. Therefore, the system is not time invariant1 KB (214 words) - 18:25, 12 September 2008
- We do not sample the function enough to get an accurate portrayal of the signal.248 B (45 words) - 11:49, 7 September 2008
- The Periodic Signal is shown below: And here is the non-periodic signal:666 B (117 words) - 14:16, 12 September 2008
- ...s say you put signal x into the system and the output is Ax. Then you put signal y into the system and the output is By. Then a linear system with signals2 KB (352 words) - 11:17, 12 September 2008
- ...follows a square effect because of the <math>k^2+1</math> that each output signal is affected by.546 B (99 words) - 07:26, 11 September 2008
- ...e system is identical to the output produced by first putting the original signal through the system and then multiplying the result by the constant.2 KB (321 words) - 19:11, 8 September 2008
- ...fted and then put through the system yields the same result as putting the signal through the system first and then shifting the output, provided the magnitu970 B (177 words) - 19:53, 8 September 2008
- '''Changing a Periodic Continuous Time Signal to a Non-Periodic Discrete Time Signal''' ...nsider the continuous time signal <math>x(t)=sin(t)</math>. Plotting this signal yields a smooth waveform that repeats itself with period <math>T=2\pi</math3 KB (536 words) - 11:07, 10 September 2008
- When we apply an input signal <math>x(t)=t^2</math>, the output is <math>y(t)=17(t^2-2t+1)</math>. When we apply a different input signal <math>x(t)=4t</math>, the output is <math>y(t)=68(t-1)</math>.2 KB (303 words) - 08:14, 9 September 2008
- A system is <b>time invariant</b> if a the time shifted input signal <math>x(t-T)</math> implies an output with equal time shift, meaning <math> ...xpect an output of <math>sin(t-1)</math>. When we apply the shifted input signal, this is exactly the output of the system.1 KB (266 words) - 08:38, 9 September 2008
- Assuming the subscript <math>k</math> denotes a time shift in the input signal, <math>Y_k[n]=(k+1)^2\delta[n-(k+1)]</math> is <b>not</b> time invariant.594 B (105 words) - 08:59, 9 September 2008
- In order to form a periodic signal, we can take a section of a non-periodic function and repeat it on to infin2 KB (377 words) - 06:59, 10 September 2008
- ...aving the signal Transformed doesn't give us the same answer as having the signal transformed then going through the Time Delay.1 KB (212 words) - 10:12, 9 September 2008
- The problem is that the cycle of signal is 1/13 which is approximately .077 which means that a timestep of .07 for ...al function, it was not nearly the correct information to display from the signal.1 KB (232 words) - 07:00, 10 September 2008
- Delay the signal by 2 => X2[n] = δ[n-4] Then run the signal through the system:2 KB (341 words) - 14:22, 11 September 2008
- ...em yelids y(t). Now, suppose input signal shifted t0, x(t-t0). Then output signal also shifted t0, y(t-t0). Then we can say a system is time-invariant. Output signal y(t) can be <math>10e^t</math> by system<br>1 KB (221 words) - 15:29, 9 September 2008
- The original signal shown in the first plot is y(t) = sin(t) with a period of <math>2\pi</math> .... No = k * <math>\frac{2\pi}{\pi/2}</math> ==> No = k * 4 so that the signal repeats itself every 4 seconds.1 KB (239 words) - 06:20, 11 September 2008
- % Periodic Signal with frequency 2*pi Hz. plot(t,y); % non-periodic Signal480 B (75 words) - 17:07, 9 September 2008
- I used sin(t) for CT periodic signal which frequency is 50hz.<br> I picked x^2 as a non-periodic signal.<br>556 B (92 words) - 15:00, 10 September 2008
- == Continuous to discrete time signal== I used the signal <math>y = cos(n)\,</math> as the signal of my graph1 KB (196 words) - 20:31, 10 September 2008
- A system is called''' time invariant''' if for any input signal x(t)(x[n]) and for any t0 belongs to R, the response to the shifted inputX( where as a system is called '''time variant''' when we find an input signal for which the condition of time invariance is violated.685 B (134 words) - 19:21, 9 September 2008
- Now the signal is run through the system first, then the time delay.830 B (154 words) - 06:44, 10 September 2008
- signal. I fixed this bug by reducing the sampling time by a factor of 20.612 B (106 words) - 08:05, 10 September 2008
- = Getting the signal -- No. 1 = The signal that I've got was taken from my own solution: y = sin(x)1,021 B (167 words) - 08:08, 10 September 2008
- === Periodic Continuous Time Signal === ...y people used in Homework 1 for their example of a periodic function. The signal repeats itself at intervals of <math> 2\pi </math>.1 KB (196 words) - 11:07, 10 September 2008
- ...r, because the sampling frequency is so large, the plotted points make the signal look as if it is not periodic. In order to correct this mistake, the varia659 B (120 words) - 15:21, 10 September 2008
- The periodic signal I used in Part A was <math>y=sin(x)</math>. To create a DT signal from the above periodic CT signal I first sampled at an integer frequency of 1. The result was a non-periodic1 KB (231 words) - 06:22, 11 September 2008
- ...{t_0}</math> introduces a time delay of <math>t_0</math> onto the function/signal x(t).) A function ("system") f is considered '''time-invariant''' iff <ma1 KB (179 words) - 15:09, 3 December 2008
- If the input signal x produces an output y then any time shifted input results in a time-shifte688 B (119 words) - 13:57, 10 September 2008
- I chose Kathleen Schremser's CT signal y(t)=sin(3/4*t). In the given signal:556 B (96 words) - 14:39, 10 September 2008
- ...is sampling at approximately the same time intervals as the period of the signal.771 B (136 words) - 15:14, 10 September 2008
- ...hifting on the input signal will result in the same shifting of the output signal. The graph below shows that the resulting signal is not a shifted input signal.979 B (159 words) - 16:25, 10 September 2008
- ...input signal is shifted along the x-axis by any amount of time, the output signal should produce the same value at <math> n + N </math> that it used to produ For the system given, let's use the signal/system corresponding to <math> X </math><sub>2</sub> for the first one and2 KB (295 words) - 15:51, 11 September 2008
- ...uld be generated from this would be <math>f[n]=5 \cos(2n)</math>. This DT signal is '''non-periodic'''. <math> \text{For }k,n \in \mathbb{N}, f[n+k] = 5 \c ...be generated from this would be <math>f[n]=5 \cos(2\pi n)</math>. This DT signal is '''periodic'''. For instance, let <math>k=1 (k\in\mathbb{N})</math> be t2 KB (312 words) - 17:53, 10 September 2008
- == CT periodic signal == An example of a periodic signal in continuous time is:1 KB (227 words) - 17:24, 10 September 2008
- I chose to use the CT (continuous time)periodic signal: y(t) = cos(t). The signal can be expressed as both periodic and non-periodic in DT (discrete time).809 B (142 words) - 17:35, 10 September 2008
- 1. CT periodic signal: 2.Non-periodic signal:231 B (36 words) - 17:29, 10 September 2008
- Given the Signal </pre><math>y=cos(pi*t)</math><pre> Lets say the Sampling rate is 1. Then the Signal is non periodic as seen in the diagram below.891 B (157 words) - 18:13, 10 September 2008
- ...n 1/26 instead. The current sampling rate causes matlab to take points the signal are at distances between the points greater than the half of the period of587 B (106 words) - 12:08, 11 September 2008
- A system is called time invariant if for any input signal x(t)(x[n]) and for any t0 belongs to R, the response to the shifted inputX( ...= 10 x(t-t0)where as a system is called time variant when we find an input signal for which the condition of time invariance is violated.2 KB (379 words) - 18:38, 10 September 2008
- ...{t_0}</math> introduces a time delay of <math>t_0</math> onto the function/signal x(t).) A function ("system") f is considered '''time invariant''' iff <ma3 KB (581 words) - 20:22, 10 September 2008
- A system is called 'time invariant' if for any input signal x(t) and for any time to that is a real number, the response to the shifted ...he system that has gone through a time shift, and i should get out another signal with the same time shift.2 KB (342 words) - 19:42, 10 September 2008
- The CT signal is y=cos(t).201 B (35 words) - 14:13, 12 September 2008
- We are given some signal <math>x_k=\delta[n-k]</math> and a system <math>f(x_k) = f(\delta[n-k])) = Thus, the signal that produces output y[n] = u[n-1] is the input <math>x[n] = \sum_{k=0}^{\i2 KB (456 words) - 11:29, 11 September 2008
- We know that x(t)=cos(t) is a periodic CT signal because it follows the rule, x(t+T)=x(t). It is periodic with a period T=<m ...yield a periodic DT signal. It is noticed that the signal is a DT periodic signal when it is sampled at rate <math>2*pi</math>,<math>pi</math>.1 KB (263 words) - 09:36, 11 September 2008
- ...ting two DT signals (one periodic and one non-periodic) from a periodic CT signal== Let <math>x(t) = sin (2\pi t),</math> which is a periodic CT signal2 KB (380 words) - 10:24, 11 September 2008
- I chose the signal <math> x[n]=e^{j\pi n} \,</math> which Jeff Kubascik posted on his HW1. Recall that this signal is periodic if <math>T = {\omega_0\over2\pi}\,</math> is rational.1 KB (186 words) - 16:24, 11 September 2008
- A CT signal posted on Homework 1 was: == Periodic Signal ==1 KB (206 words) - 09:46, 11 September 2008
- I chose to modify the signal a bit and make it y = sin(5t). :If you plot the signal in DT sampling at 5Hz you get a non-periodic signal as follows:982 B (173 words) - 10:22, 11 September 2008
- ...w2a_moellerb_ECE301Fall2008mboutin.jpg|300px|frame|center|13 Cycles of the Signal]]699 B (120 words) - 09:31, 11 September 2008
- The signal x(t)=sin(t) was chosen: Sampling at a frequency of 1 yields a non periodic signal:612 B (108 words) - 09:38, 11 September 2008
- ...ce both a periodic and non-periodic DT signal. I chose to use the tangent signal from Homework 1. ...with x[n]=tan[k+n] and k=1.5, it is possible to produce a non-periodic DT signal.979 B (158 words) - 10:46, 11 September 2008
- ...ework 1 were boring (including mine) so I thought I'd broaden the periodic signal pool. I chose the CT signal: <math>x(t) = |2*cos(.5*t)|</math> . A graph of this signal in continuous time is shown below.1 KB (207 words) - 17:25, 11 September 2008
- ...being roughly the same as the period it is little wonder that most of the signal was not captured.476 B (79 words) - 10:21, 11 September 2008
- I chose the signal: When I took a sample at 1 hz, the signal was ugly and random.798 B (136 words) - 14:54, 11 September 2008
- '''Periodic Signal in DT:''' '''Non-Periodic Signal in DT:'''3 KB (512 words) - 06:47, 12 September 2008
- Here I use the CT signal x=sin(2*pi*t) with a period of 1 sec: Producing a periodic discrete time signal from the signal above with sampling rate SR=0.01:727 B (118 words) - 16:11, 12 September 2008
- ...as Browdues has used in the previous Homework 1 assignment as my reference signal.1 KB (172 words) - 13:17, 12 September 2008
- Time Invariance describes the property of a system such that the input of signal shifted k units in time equals it's respective output shifted k units in t Now if we introduce a time delay into the input signal:969 B (167 words) - 15:36, 11 September 2008
- A system is time invariant if for any input signal x(t)/x[n] and for any time t0<math>{\in}</math>R, the response to the shift1 KB (240 words) - 11:28, 11 September 2008
- ...in time. In this system the coefficient or amplitude of the shifted output signal changes with time.1 KB (245 words) - 15:10, 12 September 2008
- ==Periodic CT Signal== ...l multiple of the frequency of the signal will result in a non-periodic DT signal.1 KB (230 words) - 16:20, 11 September 2008
- ...he sampling frequency to 0.07/250, the signal becomes periodic because the signal repeats itself.538 B (84 words) - 13:06, 11 September 2008
- <font size="3">CT signal: <math>x(t)=cos(t)</math> DT periodic signal: <math>x[n]=cos[2\pi n]</math>510 B (81 words) - 13:49, 11 September 2008
- When given a CT signal, DT signals can be produced by sampling the CT at certain intervals. For Ex Given the periodic signal <math>4cos(\pi t)</math>, The following 2 signals can be produced, one peri2 KB (239 words) - 14:00, 11 September 2008
- Signal: f(t) = 5cos(2t) Periodic DT Signal: Using a sampling rate of Ts=0.1 we get the signal565 B (81 words) - 14:08, 11 September 2008
- ...I picked for the last homework to demonstrate the sampling rate idea. My signal was tan(t). If you sample this function at a rate of <math>\pi</math>, eve ...sum were taken to infinity, the shift of 1 would result in the exact same signal, thus it would be periodic.1 KB (208 words) - 14:07, 11 September 2008
- Since both cascades produce the same output signal, this is an example of a time invariant system.1 KB (270 words) - 15:06, 11 September 2008
- ...passes through a system and then is time shifted, it is equal to when the signal is time shifted and then passed through the system. System --> sqrt[of signal] = Time invariant871 B (183 words) - 14:20, 11 September 2008
- ...e vector interval Ts = 0.07 sec is too small compared to the period of the signal which is 1/13 <math>\approx</math> 0.0769 sec. This bug can be fixed by let573 B (96 words) - 14:13, 11 September 2008
- So the output of the signal is:659 B (121 words) - 14:16, 11 September 2008
- ...ne of the signals in the left column, then the output is the corresponding signal in the right column:2 KB (368 words) - 10:26, 12 September 2008
- %Periodic signal %Non-Periodic Signal1 KB (223 words) - 09:59, 12 September 2008
- ...ccurs because the sampling rate is too small. The period of the sinusoidal signal given is 1/13 = 0.0769 and the sampling period set is 0.07. It is clear to552 B (87 words) - 14:59, 11 September 2008
- %Periodic signal %Periodic signal turned non-periodic by setting the sampling period to 0.1642 B (88 words) - 15:45, 11 September 2008
- First we will take a signal and go through the system, then time delay it:1 KB (241 words) - 16:05, 11 September 2008
- == Sampling of CT Signal to Yield a DT Signal == Periodic Signal sampled to become Non-Periodic:774 B (126 words) - 13:28, 12 September 2008
- <b>Changing a Periodic Continuous Time Signal to a Non-Periodic Discrete Time Signal</b> The signal I chose for this part can be found [[HW1.4 Wei Jian Chan - Periodic and Non1 KB (186 words) - 16:07, 11 September 2008
- ==Periodic signal revisited==808 B (131 words) - 19:18, 11 September 2008
- A system is called time invariant if shifting it's input signal in time results in the same time shift propagated to its output.1 KB (197 words) - 16:59, 11 September 2008
- A system is time invariant if for a signal X(t) or X[n] and time t0 , a shifted input of X(t-t0) yields in a shifted o647 B (121 words) - 18:35, 11 September 2008
- 1. By sampling at different frequencies the signal <math>y=sin(x)\!</math> can appear as both periodic and non-periodic in DT. ...<math>x=[0, 10]\!</math> we can turn a non-periodic signal into a periodic signal:1 KB (209 words) - 10:10, 12 September 2008
- A linear system is a system that an output of a certain signal is the sum of all the input signals. This is exactly the same as the proper2 KB (290 words) - 19:23, 11 September 2008
- ...me invariant if for any input signal <math>\,x(t)\,</math> yielding output signal <math>\,y(t)\,</math> and for any <math>\,t_o\in\mathbb{R}\,</math>, the re2 KB (276 words) - 20:05, 11 September 2008
- I choose y(t)=cos(t) as my continous signal. ...ple the signal y(t)=cos(t) at 100 Hz and so we get the following discrete signal which is periodic1 KB (207 words) - 21:44, 11 September 2008
- ..., the time-shifted output signal must correspond to the time-shifted input signal.1 KB (213 words) - 20:13, 11 September 2008
- ...samples is very high. This results into skipping of certain values of the signal.651 B (108 words) - 21:59, 11 September 2008
- The sampling rate Ts is too large. It only displays one cycle of the signal. By lowering it to 0.0007 all of the cycles are shown.132 B (25 words) - 03:51, 12 September 2008
- The CT signal <math>\cos{x}</math> can be both periodic and non-periodic in DT. With a sampling rate of <math>1</math> the DT signal looks like this:371 B (61 words) - 04:13, 12 September 2008
- In HW1 I used the signal cos(t-2) so I will use that as my example signal. ...4] shift and add the signal together multiple times we can get a periodic signal with period 2.397 B (76 words) - 05:07, 12 September 2008
- Pick a CT periodic signal that was posted on Rhea as part of homework 1, and create two DT signals, o Using Xujun Huang's function <math>e^t</math> I was able to create a periodic signal.912 B (139 words) - 07:02, 12 September 2008
- The above image illustrates a periodic CT triangle signal with a frequency of one radian per second. If this was mapped to a DT signal it would be periodic and look like:539 B (82 words) - 06:21, 12 September 2008
- ...ultiply the 2 outputs by a constant, and add them together to get my final signal i should get the same if i multiply the two input signals by the constant f2 KB (285 words) - 07:21, 12 September 2008
- ...sent through the system. In the other, the time delay must come after the signal being sent through the system. If the returned output is equal in both case1 KB (222 words) - 07:00, 12 September 2008
- ==Part 1: DT Signals From one CT Signal== ...rated in homework 1.4, <math>sin(x)</math>, to create two DT signals. One signal will be periodic, and the other will not.2 KB (433 words) - 08:01, 12 September 2008
- Since z[n] = w[n] the signal is time invariant.492 B (104 words) - 07:42, 12 September 2008
- I used my CT signal <math>x(t) = 3\cos(4t + \frac{\pi}{3})</math> from homework 1. The periodic signal was created by sampling .001 from 0 to 5494 B (74 words) - 08:13, 12 September 2008
- I used the signal <math> x = sin(t)\,</math> I chose the signal <math>x(t) = t^2\,</math> to make a periodic signal.1 KB (183 words) - 07:45, 12 September 2008
- ...ere is a bug in this code. The timestep in this case makes the part of the signal that is plotted is considered to small to get a full sample.853 B (162 words) - 12:08, 12 September 2008
- A system is time invariant if an input signal x(t) corresponds to the output signal y(t) despite any scaling due to time.378 B (67 words) - 13:17, 12 September 2008
- ...input signal x(t) can be shifted by (t-to) and its output will be the same signal, yet it will be shifted the same throughout the system.751 B (146 words) - 12:22, 12 September 2008
- title('CT Signal'); % change sampleing rate to be periodic DT signal1 KB (183 words) - 09:21, 12 September 2008
- ...riant if a shift in the input signal produces the same shift in the output signal.814 B (148 words) - 08:48, 12 September 2008
- =Parte Dos - Make a Periodic Signal from Non-periodic Source=1 KB (217 words) - 08:58, 12 September 2008
- ...nitude applied to it. Also if two signals are added it would be as if each signal had went through the system and then had been added.947 B (193 words) - 14:54, 12 September 2008
- In the variant example the amplitude of the signal depends on time so it is time variant392 B (72 words) - 10:10, 12 September 2008
- Let us check if the following signal is linear. Let us check if the following signal is linear1 KB (250 words) - 10:42, 12 September 2008
- 1.This is a sine function of period 2. Function is sin(pi*t). Continuous Signal. 2. '''Periodic DT Signal'''This is the discrete signal of the same function in 1 with sampling time of 0.075. I got the diagram on642 B (86 words) - 10:23, 12 September 2008
- ...espectively, then added together and passed through a system that yields a signal '''<math>Z(t)</math>'''. ...>C_2\in \mathbb{C}</math> respectively, and then added together yielding a signal '''<math>W(t)</math>'''.2 KB (401 words) - 16:12, 12 September 2008
- ...one posted under Hw 1.4 David Hartmann. I use period of 10 to create this signal to be a periodic one. The plot is shown below:310 B (57 words) - 11:05, 12 September 2008
- Periodic signal ...of the frequency of the signal will result in a non-periodic Discrete Time signal.775 B (125 words) - 17:10, 12 September 2008
- Choose the signal <math>x(t)=cos(t)</math> which is periodic. This is <math>x(t)=e^{-t}cos(20t)</math> as the nonperiodic signal.851 B (147 words) - 15:14, 12 September 2008
- "A system is called "time invariant" if for any input signal x[n] and for any <math>t_0 \epsilon \mathbb{R}</math>, the response to the369 B (62 words) - 13:01, 12 September 2008
- Now suppose we pass the signal through the system first and then delay it842 B (149 words) - 13:12, 12 September 2008
- ...variant Systems are systems that produce the same output for a given input signal that has a time shift as it would without the time shift except for that th ...then inputing it into the system and comparing the results to imputing the signal x(t) into the system and then inputing that results into the time-delay cir821 B (152 words) - 13:44, 12 September 2008
- With the value set to T0, It is sampling the signal once every period. To solve this just make the value of T0 very small compa244 B (47 words) - 13:39, 12 September 2008
- The output of the signal x1(t)=t is y1(t)=2(t+3)=2t+6. The output of the signal x2(t)=t-1 is y2(t)=2(t+3-1)=2t+4.832 B (168 words) - 14:05, 12 September 2008
- The CT signal that I have selected is x=sin(t).219 B (34 words) - 14:07, 12 September 2008
- == Create Periodic Signal ==439 B (66 words) - 14:33, 12 September 2008
- ...e signal whether you play it at 10:01 AM or 10:06 AM. This is because the signal is the same if you listen to the song now or later. This is a 5 minute tim ...on your T.V. at 10:06 AM. This is a 5 minute time shift which affects the signal that the observer sees.549 B (107 words) - 14:25, 12 September 2008
- ...is '''not Time-invariant''' as it is determined by the dealy of the Input Signal97 B (17 words) - 14:33, 12 September 2008
- ...of <math>t_0</math> yields <math>x(t-t_0)=(t-t_0)+4</math> now this input signal through the system yields <math>y(t)=5((t-t_0)+4)=5(t-t_0)+20</math>1 KB (196 words) - 14:34, 12 September 2008
- == A CT periodic signal sampled at different frequencies == == Making periodic signal by shifting and summing aperiodic signals ==769 B (126 words) - 15:32, 12 September 2008
- by sampling every <math>2*pi</math> or changing the signal to760 B (145 words) - 15:10, 12 September 2008
- The system is defiantly not time invariant. When the signal is shifted the output is shifted also but a different magnitude is applied496 B (91 words) - 15:34, 12 September 2008
- ...ting two DT signals (one periodic and one non-periodic) from a periodic CT signal== I choose <math>x(t) = sin (2\pi t),</math> which is a periodic CT signal649 B (104 words) - 16:13, 12 September 2008
- the signal is time invariant720 B (144 words) - 16:43, 12 September 2008
- ...shift in the input signal results in an identical time shift in the output signal. ...of the system is x[n] , then y[<math>n_0</math>-n] is the output when the signal is x[<math>n_o</math>- n].403 B (84 words) - 16:25, 12 September 2008
- If for any signal '''<math>X(t)\Rightarrow Y(t)</math>''' implies that '''<math>X(t - t_o)\Ri ...up 10 minutes late to lecture, he will have missed 10 minutes of lecture (signal). Therefore, ECE 301 lectures are a "time-variant" system.1 KB (204 words) - 16:51, 12 September 2008
- == PERIODIC AND NON-PERIODIC DT SIGNALS FROM A CT SIGNAL == %periodic CT signal939 B (153 words) - 18:26, 12 September 2008
- A system is time invariant if for any time shifted input signal the system produces a shifted output such that if an input <math>x(t)</math '''Time Invariant Signal'''813 B (172 words) - 17:22, 12 September 2008
- The periodic DC signal at this frequency would be: The non-periodic DC signal with frequency @ 0.6519 B (81 words) - 18:12, 12 September 2008
- The periodic part of the CT signal With the increase in scaling we can see the non periodic part of the above signal is as belows255 B (44 words) - 17:55, 12 September 2008
- ...re separately multiplied by constants a and b and the added .The resulting signal after addition can be called z(t).1 KB (282 words) - 18:13, 12 September 2008
- ...current time. The <math>t-1\,</math> is just the value of the time when a signal is inputted into a system975 B (176 words) - 11:55, 30 January 2011
- Part B) From the data ,we deduce that the system is linear and the input signal is u [n]310 B (52 words) - 18:56, 12 September 2008
- Therefore the System modifies the signal accordingly:806 B (114 words) - 10:02, 16 September 2008
- and then there exists an <math> M\!</math> for the ouput signal y(t) such that ...signal is exp(t)*cos(t), which increases in value as t increases, and this signal is quite obviously unbounded. Mathematically, this means that there exists1 KB (251 words) - 06:44, 19 September 2008
- A system is said to be "causal" if at any given time, the output signal depends only on the present and/or past input signals. ...ausal" if at any given time, the output signal depends on the future input signal.387 B (71 words) - 11:52, 16 September 2008
- ...efore, the input signal <math> \,\ x(t) = cos(2t) </math> yields an output signal of <math> \,\ z(t) = tcos(2t) </math>1 KB (248 words) - 13:29, 16 September 2008
- ...l in present or past time. The output signal does not depend on the input signal in future time. ...signal is input into the system and the output signal depends on the input signal in future time, then the system is non-causal.776 B (146 words) - 05:27, 17 September 2008
- ...d input yeilds a bounded output. This means that if you can take an input signal whose value does not increase to infinity as x -> infinity, then the output ...nput yeilds an unbounded output. This means that if you can take an input signal whose value does not increase to infinity as x -> infinity, then the output545 B (101 words) - 05:53, 17 September 2008
- Its response to this signal is <math>t*e^{-2jt}</math> which can be rewritten as:318 B (61 words) - 06:27, 17 September 2008
- ...in present and past time. The output signal does not depend on the input signal in future time, otherwise it is considered non-causal.591 B (112 words) - 16:26, 17 September 2008
- A system is called time invariant if for any input signal x(t) yielding output y(t) and for any time <math>t_0</math> the output to t2 KB (324 words) - 17:50, 17 September 2008
- : The Signal is Linear :Since the system is linear you can split the signal in two parts527 B (109 words) - 08:35, 18 September 2008
- Take the input signal to be <math>\frac{1}{2}(x_1(t)+x_2(t))</math>.981 B (197 words) - 11:05, 18 September 2008
- What, then, is the system's output for the input signal x(t) = cos(2t)? ...factors, it seems that the input x(t) = cos(2t) will result in the output signal y(t) = 1/(cos(2t)).1 KB (226 words) - 12:07, 19 September 2008
- ...usal system is dependent only on the present and past samples of the input signal, '''X(n)''' and not on any future samples of the input624 B (128 words) - 13:45, 18 September 2008
- A system is called "'''time invariant'''" if for any input signal x(t) in continuous time or x[n] in discrete time and for any time <math>t_0 A system is called "'''time variant'''" if for any input signal x(t) in continuous time or x[n] in discrete time and for any time <math>t_01 KB (193 words) - 18:59, 18 September 2008
- A system is called time invariant if for any signal x(t)190 B (36 words) - 00:30, 19 September 2008
- ...shift in the input signal results in an identical time shift in the output signal." - (Oppenheim Willsky pgs. 50-51) ...ift in the input signal results in some different time shift in the output signal.1 KB (177 words) - 05:16, 19 September 2008
- ...signal, and the output is equal to that same scalar times the transformed signal. ...signal, and the output is equal to that same scalar times the transformed signal.391 B (70 words) - 05:45, 19 September 2008
- ...stem is stable if '''any''' bounded input signal produces a bounded output signal.<br> A bounded signal is any signal that given a number K, for all t, |x(t)| <= K182 B (33 words) - 07:14, 19 September 2008
- So when the signal is run through the system the following is what is produced371 B (77 words) - 08:09, 19 September 2008
- "A system is called "time invariant" if for any input signal x[n] and for any <math>t_0 \epsilon \mathbb{R}</math>, the response to the382 B (67 words) - 11:46, 19 September 2008
- We can use this to represent our input signal as follows:838 B (157 words) - 11:55, 19 September 2008
- ==Periodic CT Signal, Fourier Series Coefficients== * [[HW4.1 Wei Jian Chan_ECE301Fall2008mboutin]] CT signal in terms of sines and cosines.12 KB (1,544 words) - 11:27, 16 September 2013
- ...n input signal x(t) into the system gives y(t) then also for a given input signal x(t-to), for to as a real number, the output is y(t-to).520 B (99 words) - 11:53, 30 January 2011
- CT Periodic Signal : <math>x(t) = \cos(3\pi t) + \sin(4\pi t)\,</math> The following is the coefficient of the signal:784 B (140 words) - 10:34, 20 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == == CT signal ==1 KB (217 words) - 11:04, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == == Define a Periodic CT signal and compute its Fourier series coefficients ==1,021 B (156 words) - 10:58, 16 September 2013
- == "Guessing the Periodic Signal" == Supposing we are given a signal x(t)615 B (95 words) - 17:51, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == CT Periodic Signal : <math>x(t) = \cos(3\pi t) + \sin(4\pi t)\,</math>1 KB (197 words) - 10:59, 16 September 2013
- CT Periodic Signal : <math>x[n] = 5\cos(6\pi n + \pi) + 7\cos(3\pi n)\,</math>1 KB (207 words) - 12:07, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == CT Signal:1 KB (192 words) - 10:58, 16 September 2013
- DT signal:876 B (156 words) - 15:56, 22 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == CT signal:1 KB (242 words) - 10:58, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == == Signal ==1 KB (186 words) - 10:58, 16 September 2013
- :<math>a0=average of signal = 0 \,</math> ...first term and since there are no other terms a2=a3=0. Then a0= average of signal.2 KB (415 words) - 11:46, 23 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == ==CT Periodic Signal==671 B (107 words) - 10:57, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL ==778 B (122 words) - 10:57, 16 September 2013
- ...fined in Question 1 using H(s) and the Fourier series coefficients of your signal.1 KB (223 words) - 07:30, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL ==2 KB (306 words) - 10:57, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == ==The Signal==2 KB (384 words) - 10:56, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == Let the input signal be783 B (123 words) - 10:59, 16 September 2013
- == Response of the system to the signal defined in Question 1 ==865 B (174 words) - 08:52, 27 September 2008
- A Signal for which the output signal is constant times the input is referred as1 KB (215 words) - 14:56, 26 September 2008
- <pre>Input CT signal: x(t) = 3cost+sin2t</pre>.229 B (44 words) - 10:40, 24 September 2008
- ==Periodic DT Signal== The following plot shows two periods of the periodic DT signal <math>x[n]</math>, a sawtooth:1 KB (162 words) - 13:40, 24 September 2008
- For periodic DT signal, x[n] with fundamental period N: Let us look for the Fourier series coefficients for the DT signal <big><math>x[n] = cos(3\pi n)</math></big>1 KB (230 words) - 14:22, 26 September 2008
- ==DT Signal Fourier Coefficients== Let's make up a signal.2 KB (271 words) - 17:36, 25 September 2008
- Input <math>x[n]</math> is the following signal:1 KB (222 words) - 13:55, 24 September 2008
- ==CT Signal & its Fourier coefficients== Lets define the signal369 B (68 words) - 21:38, 23 September 2008
- == Fourier Series Coefficients for a DT signal == Lets look at the signal <math>\,x[n] = 7cos[5\pi n]</math>650 B (95 words) - 07:26, 24 September 2008
- == A Periodic CT signal and it's Fourier Coefficients == '''Signal:'''143 B (21 words) - 10:15, 24 September 2008
- ==Response to a Signal from Question 1== I will use my signal from Question 1.2 KB (344 words) - 13:40, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == == Periodic CT Signal and Its Fourier Coefficients ==3 KB (464 words) - 10:58, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == == The signal used ==834 B (129 words) - 10:56, 16 September 2013
- ===Signal power and energy === ...008mboutin| Example of how to take the Fourier transform of a non-periodic signal]]2 KB (243 words) - 08:04, 21 November 2008
- == Example of Computation of Fourier series of a CT SIGNAL == I chose the signal: <math>f(t) = (3+j)cos(2t) + (10+j)sin(7t)\!</math>2 KB (384 words) - 10:55, 16 September 2013
- <font size="3">Supposing we are given a signal <math>x(t)</math> Specify a signal that satisfies the given conditions.369 B (58 words) - 16:46, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == Signal Coefficients:2 KB (360 words) - 10:55, 16 September 2013
- Input Signal: <math> x(t) = 5cos(2t) + 3sin(4t) \!</math>1 KB (175 words) - 17:18, 24 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == ==The signal==2 KB (429 words) - 10:55, 16 September 2013
- ==Determine the Periodic Signal== A periodic signal x[n] has the following characteristics:2 KB (351 words) - 20:45, 24 September 2008
- CT Periodic Signal : <math>x(t) = \cos(3\pi t) + \sin(4\pi t)\,</math>1 KB (214 words) - 19:15, 24 September 2008
- CT Periodic Signal : <math>x[n] = 5\cos(6\pi n + \pi) + 7\cos(3\pi n)\,</math>1 KB (218 words) - 19:15, 24 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == CT Periodic Signal : <math>x(t) = 1+\sin \omega_0 t + \cos(2\omega_0 t+ \frac{\pi}{4})</math>2 KB (250 words) - 10:54, 16 September 2013
- Let <math>x[n]\,</math> be a periodic DT signal with fundamental period N. Now consider the signal <math>x[n]=sin(3 \pi n)\,</math>907 B (155 words) - 06:49, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == ==Define a periodic CT signal and compute its Fourier series coefficients.==837 B (141 words) - 10:56, 16 September 2013
- ==Define a periodic DT signal and compute its Fourier series coefficients. == Let the signal be480 B (88 words) - 18:22, 26 September 2008
- ...fined in Question 1 using H(s) and the Fourier series coefficients of your signal. CT signal :1 KB (241 words) - 18:42, 26 September 2008
- ==“guess the periodic signal” question== Signal215 B (38 words) - 18:34, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL ==863 B (144 words) - 10:54, 16 September 2013
- The systems response to this signal would be... The systems response to this signal by direct computation would be...2 KB (339 words) - 07:23, 25 September 2008
- ==Response to a Signal== My signal in Part 1 was: <math>x(t)=sin(\pi t) + cos(2\pi t) </math>731 B (144 words) - 06:42, 25 September 2008
- ==Composing a Signal==210 B (32 words) - 07:25, 25 September 2008
- 1. This signal is the math equivalent of a synonym for the word 'strange'. 2. This signal is never less than 0, but is always less than 8.801 B (140 words) - 07:43, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == ==CT Signal==2 KB (363 words) - 10:56, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL ==966 B (160 words) - 10:53, 16 September 2013
- ==Guess the Signal== Given the first property of the signal, we can rewrite the bounds of summation in the second property since the ze1 KB (203 words) - 17:19, 25 September 2008
- ===Response to a signal===971 B (188 words) - 08:43, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == Given the periodic CT signal2 KB (410 words) - 10:53, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == ==CT signal==1 KB (216 words) - 11:02, 16 September 2013
- ===Signal=== 4. The signal is never more than 6 or less than -6213 B (37 words) - 09:37, 25 September 2008
- ==DT signal ==827 B (147 words) - 09:36, 25 September 2008
- 1. This signal starts at zero and moves like the Ocean 2. This signal is never less than 0, but is always less than 4.488 B (82 words) - 09:45, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == ==Signal==2 KB (279 words) - 10:54, 16 September 2013
- 1. The signal has only two non-zero Fourier coefficients (-1 and 1). 2. The fundamental period of the signal is 8.1 KB (231 words) - 18:07, 25 September 2008
- ==Periodic Signal Properties == 5. Signal is Even1 KB (219 words) - 10:32, 25 September 2008
- == Guess the signal == 1. DT signal x[n] has a period of 2.590 B (97 words) - 10:39, 25 September 2008
- The signal found in Question 1 was:<br> To find the system's response to the signal, simply multiply it by the system function:<br>1 KB (275 words) - 11:52, 25 September 2008
- == Define a Periodic DT Signal and Compute the Fourier Series Coefficients == I am going to choose a sine signal, since there have been many cosines done already.3 KB (405 words) - 12:42, 25 September 2008
- == Computing the Fourier series coefficients for a Discrete Time signal x[n] ==900 B (178 words) - 12:47, 25 September 2008
- == RESPONSE OF SYSTEM TO SIGNAL DEFINED IN QUESTION 1 == Signal used in question 1:1 KB (238 words) - 08:31, 26 September 2008
- == Guess the Periodic Signal==261 B (42 words) - 16:17, 26 September 2008
- == Compute the Response of My Signal from Question 2 == Signal: <math>x[n] = 2\sin(\pi n + \frac{\pi}{2}) + 4\sin(\frac{\pi}{2} n + \pi)\2 KB (308 words) - 14:13, 25 September 2008
- Suppose a DT signal x[n] satisfies672 B (117 words) - 13:08, 25 September 2008
- == Response of y[n] to the signal I defined in Question 2 using H[z] and the Fourier series coefficients ==1 KB (242 words) - 13:11, 25 September 2008
- == Guess the Periodic Signal == A certain periodic signal has the following properties:2 KB (328 words) - 14:01, 25 September 2008
- == GUESS THE PERIODIC SIGNAL ==422 B (67 words) - 13:28, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == == Example of a periodic CT signal ==2 KB (283 words) - 10:55, 16 September 2013
- == Definition of fourier transform for DT signal == == Example of a periodic DT signal ==2 KB (374 words) - 14:27, 25 September 2008
- Given the following periodic DT signal which is an infinite sum of shifted copies of a non-periodic signal, compute its Fourier series coefficients.2 KB (375 words) - 15:10, 25 September 2008
- '''Solution:''' A periodic DT signal can be expressed as a Fourier series in the following manner: ...} = \frac{\pi}{2}</math> is also known as the fundamental frequency of the signal.)2 KB (313 words) - 14:17, 25 September 2008
- '''b)''' Compute the response of f to the signal x[n] found [[HW4.2_Brian_Thomas_ECE301Fall2008mboutin|here]] by using H(z)2 KB (355 words) - 16:48, 25 September 2008
- 1. The signal is heavily used in sampling. The signal is the (normalized) sinc function: <math>\frac{sin(\pi x)}{\pi x}</math>389 B (63 words) - 14:52, 25 September 2008
- <math>N = 2</math> due to the signal switching between 1 and -1.<br><br>770 B (140 words) - 15:12, 25 September 2008
- === b) Response of Signal in Question 1 === Unfortunately, I did not make a DT signal for Parts 1/2. Instead of going back and redoing my work, I am going to "s2 KB (390 words) - 07:56, 26 September 2008
- == Guess the signal == Given that the definition of a signal defined by fourier transforms is shown like:1 KB (203 words) - 16:00, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == ==Periodic CT Signal==1 KB (205 words) - 10:56, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL ==1 KB (210 words) - 11:03, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == Defines the Fourier series of a periodic ct signal as911 B (165 words) - 11:03, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == Let the signal be1 KB (215 words) - 10:59, 16 September 2013
- '''Problem:''' Find the periodic DT signal x[n], given:1 KB (186 words) - 17:47, 25 September 2008
- ...xpressed as a sum of complex exponentials, we need only multiply the input signal by H(t).1 KB (207 words) - 18:48, 25 September 2008
- == Guess the Periodic Signal == 5. The value of the signal at <math>\,n=0\,</math> is zero.1 KB (250 words) - 20:40, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == == The Signal ==1 KB (182 words) - 11:03, 16 September 2013
- x(t) is a real and even signal.681 B (108 words) - 19:13, 25 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == == Signal ==984 B (159 words) - 11:04, 16 September 2013
- == Signal x(t) ==245 B (42 words) - 20:49, 25 September 2008
- == Signal ==967 B (170 words) - 14:35, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == For a CT signal891 B (142 words) - 11:01, 16 September 2013
- Consider the signal:876 B (173 words) - 04:45, 26 September 2008
- Periodic DT Signal686 B (122 words) - 05:01, 26 September 2008
- Periodic signal 3. Signal not less than 0, but always less than 6270 B (41 words) - 05:16, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == == Define a CT Signal and its Fourier Series Coefficients ==777 B (123 words) - 11:05, 16 September 2013
- ==Guess Signal== The signal is DT periodic with period of 4938 B (182 words) - 07:09, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL ==885 B (159 words) - 11:01, 16 September 2013
- 3. -9 <= signal <=9248 B (41 words) - 07:06, 26 September 2008
- ...fined in Question 1 using H(s) and the Fourier series coefficients of your signal== Signal defined in Question 1:2 KB (349 words) - 08:25, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == periodic signal: <math> \begin{align} x(t) = 32 + 8sin(2\pi t) + 22cos(2\pi t) + 2cos(2\pi1 KB (163 words) - 11:05, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == Signal Coefficients:938 B (158 words) - 11:02, 16 September 2013
- ...fined in Question 2 using H(z) and the Fourier series coefficients of your signal= Signal defined in Question 1:1 KB (241 words) - 09:04, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == Let us take the periodic, CT signal: <math>3cos(4\pi t) + e^{j\frac{2\pi}{5}t}</math>989 B (173 words) - 11:06, 16 September 2013
- The signal used in question 1:837 B (166 words) - 09:55, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == ==Periodic CT Signal==806 B (120 words) - 11:06, 16 September 2013
- 1. DT signal is real and even with period N=12 Because the signal is even, a2=a(N-2) and a3=a(N-3. Using Parseval's relation, we find that t578 B (116 words) - 10:13, 26 September 2008
- == Compose a "Guess the periodic signal question: ==143 B (23 words) - 10:47, 26 September 2008
- We are given the following information about a signal x[n]:504 B (78 words) - 10:58, 26 September 2008
- The signal used in Q1 is: So, the response of this system to the signal I defined in Q1 is:910 B (185 words) - 14:36, 26 September 2008
- In order to find the period of the signal below, we need to find a value of K that will make N an integer.560 B (103 words) - 12:59, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == The function y(t) in this example is the periodic continuous-time signal cos(t) such that1 KB (195 words) - 11:07, 16 September 2013
- ==The Signal== Consider the signal which is given by the following values and limits:1 KB (261 words) - 13:32, 26 September 2008
- == Guess the Periodic Signal == * The period of the DT signal x[n] = 2637 B (101 words) - 13:22, 26 September 2008
- Signal from question 2:1,016 B (194 words) - 15:50, 26 September 2008
- == get the response of H(s) to signal proposed in previous question ==780 B (146 words) - 14:19, 26 September 2008
- == Signal ==944 B (140 words) - 14:11, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == Let the signal <math>x(t) = 5cos(3\pi t) + sin(\pi t)\,</math><br>1 KB (201 words) - 11:06, 16 September 2013
- 1. x[n] is a real and even signal800 B (136 words) - 15:12, 26 September 2008
- == A Periodic DT Signal == The signal above x[n] is periodic with period N.1 KB (275 words) - 16:31, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == ==Define a Periodic CT Signal and Compute its Fourier Series Coefficients==1 KB (228 words) - 11:07, 16 September 2013
- The signal used in Q2 was <math>x[n]=3+sin\bigg(\frac{\pi}{2}n\bigg)</math> So, the response of this system to the signal I defined in Q2 is:842 B (168 words) - 14:55, 26 September 2008
- ==Computing the Response of the Signal from Q1 using H(s)== When a periodic signal represented as a linear combination of complex exponential is inputted into1 KB (239 words) - 17:50, 26 September 2008
- Suppose a DT signal satisfies the following properties:2 KB (426 words) - 15:21, 26 September 2008
- == Guess the Periodic Signal ==199 B (30 words) - 15:43, 26 September 2008
- == DT signal & its Fourier Coefficients ==1 KB (200 words) - 17:10, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == == A periodic CT signal ==1 KB (188 words) - 11:08, 16 September 2013
- Then we can calculate the system's response to a signal using H[z] and the fourier coefficients for the system. My signal from part 2 has fourier coefficients:1 KB (203 words) - 16:23, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == For the CT signal:1 KB (215 words) - 11:04, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL ==923 B (155 words) - 11:07, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == ==Definition of Periodic CT Signal==877 B (147 words) - 10:53, 16 September 2013
- In this last part, you just take my signal from part (a):2 KB (334 words) - 16:10, 26 September 2008
- ==Guessing a periodic signal based on a few properties given== ==Finding the signal based on the properties==1 KB (260 words) - 16:57, 26 September 2008
- DT Signal: 1. Signal is periodic with N = 4529 B (79 words) - 16:33, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == == CT Signal ==2 KB (311 words) - 10:57, 16 September 2013
- == Example of Computation of Fourier series of a CT SIGNAL == Lets define the signal931 B (147 words) - 10:59, 16 September 2013
- == Periodic DT Signal ==462 B (89 words) - 16:43, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == Find the Fourier series coefficients of a CT signal.2 KB (291 words) - 10:54, 16 September 2013
- Rewriting the periodic signal in Question 1, <br><br>2 KB (276 words) - 17:34, 26 September 2008
- ===Signal Clues=== 4. The norm of the output signal is never more than <math> \pi +1 </math>271 B (47 words) - 16:39, 26 September 2008
- where v(t) is an input signal dependent on the parameter of time. The response of this system to my signal y(t) = cos(t) from HW4.1 yields the output1 KB (233 words) - 17:43, 26 September 2008
- We have a DT signal x[n] such that:719 B (121 words) - 16:44, 26 September 2008
- Suppose we have a LTI CT signal y(t)=2x(t) ==Response of the Signal and Fourier Series Coefficients==1 KB (214 words) - 17:41, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == ==Periodic CT Signal==863 B (140 words) - 11:08, 16 September 2013
- ==Signal Response== Now we need to find the LTI system above's response to my signal from section 4.1. The response can be found with the equation1 KB (204 words) - 17:09, 26 September 2008
- = Fourier series coefficients for DT signal = ==DT Signal==818 B (140 words) - 17:14, 26 September 2008
- ==Guess the Periodic Signal== Find a DT signal that satisfies these properties:369 B (57 words) - 17:40, 26 September 2008
- ===The CT LTI Signal=== HW 4.1 signal550 B (110 words) - 17:36, 26 September 2008
- A signal x(t)198 B (35 words) - 17:45, 26 September 2008
- and the input signal, <br><br>1 KB (261 words) - 18:24, 26 September 2008
- ==CT LTI signal: == == Signal from Question 1 ==709 B (143 words) - 18:37, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == = Fourier series coefficients for CT signal =822 B (139 words) - 10:57, 16 September 2013
- *4 The signal is ... real and odd *Since it is real and odd the base signal is a <math>\cos</math>498 B (82 words) - 17:49, 26 September 2008
- Suppose we are given the following information about a signal x(t): Two signals that would satisfy these coniditions is the input signal992 B (159 words) - 18:33, 26 September 2008
- Signal defined in Question 1:921 B (187 words) - 18:40, 26 September 2008
- ==Guess The Signal== 1. The signal is periodic with a period of 3 seconds416 B (69 words) - 18:18, 26 September 2008
- Guessing the periodic signal:994 B (178 words) - 18:44, 26 September 2008
- I'm not quite sure how to complete my problem. The signal I'm trying to create is <math>x[n] = sin(3 \pi n + \frac{\pi}{2})</math>.293 B (49 words) - 19:24, 26 September 2008
- suppose we have the following information about a signal x(t):271 B (39 words) - 18:51, 26 September 2008
- == Example of Computation of Fourier series of a CT SIGNAL == CT Periodic Signal :1 KB (169 words) - 11:09, 16 September 2013
- ...system to the signal using H(s) and the Fourier series coefficients of the signal.<br><br>905 B (182 words) - 19:11, 26 September 2008
- Response to a Signal : multiplying each term of input signal by <math>H(j\omega)</math>1 KB (205 words) - 19:22, 26 September 2008
- Periodic Signal681 B (108 words) - 19:29, 26 September 2008
- ===Guessing The Periodic Signal===1 KB (186 words) - 20:38, 26 September 2008
- == Example of Computation of Fourier transform of a CT SIGNAL ==2 KB (270 words) - 12:24, 16 September 2013
- == Example of Computation of Fourier transform of a CT SIGNAL == Specify a signal x(t) and compute its Fourier transform using the integral formula.( Make a913 B (139 words) - 12:24, 16 September 2013
- == Example of Computation of Fourier transform of a CT SIGNAL == Compute the Fourier transform of the following CT signal using the integral formula:2 KB (279 words) - 12:25, 16 September 2013
- Compute the inverse Fourier transform of the following signal using the integral formula:2 KB (384 words) - 12:42, 16 September 2013
- == Example of Computation of Fourier transform of a CT SIGNAL == Compute the fourier transform of this signal below:1 KB (215 words) - 12:26, 16 September 2013
- == Example of Computation of Fourier transform of a CT SIGNAL ==1 KB (213 words) - 12:26, 16 September 2013
- ...ggle to understand how to prove whether or not a signal is periodic if the signal is written as the sum of shifted functions. A good example of this type of Is the signal periodic?343 B (61 words) - 14:22, 6 October 2008
- == Example of Computation of Fourier transform of a CT SIGNAL ==759 B (126 words) - 12:27, 16 September 2013
- == Example of Computation of Fourier transform of a CT SIGNAL == == Signal ==1 KB (171 words) - 12:28, 16 September 2013
- == Example of Computation of Fourier transform of a CT SIGNAL == == Signal ==1 KB (260 words) - 12:28, 16 September 2013
- == Example of Computation of Fourier transform of a CT SIGNAL == Let the signal x(t) be equal to:1 KB (191 words) - 12:29, 16 September 2013
- == Example of Computation of Fourier transform of a CT SIGNAL == The Fourier transformation of the signal x(t) is defined as2 KB (281 words) - 12:29, 16 September 2013