• ...ved by the use of a periodic impulse train multiplied by a continuous time signal, <math>x(t)</math>. The periodic impulse train, <math>p(t)</math> is refer
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  • ...continuous-time signal to discrete-time signal, process the discrete-time signal using a discrete-time system and convert it back to continuous time. ...and X(j<math>\omega\,</math>) be the continuous Fourier transform of that signal. Then,
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  • ...the uniformly spaced discrete samples are a complete representation of the signal if this bandwidth is less than half the sampling rate. ...signal and <math>X(W)\,</math> be the continuous Fourier transform of that signal
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  • Let <math>x(t)</math> be a signal with <math>X(\omega) = 0</math> when <math>|\omega| > \omega_m</math>. <math>\omega_m</math> Maximum frequencye for a band limited signal
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  • ...the uniformly spaced discrete samples are a complete representation of the signal if this bandwidth is less than half the sampling rate. ...signal and <math>X(w)\,</math> be the continuous Fourier transform of that signal (which exists if <math>x(t)\,</math> is square-integrable)
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  • ...AB. By use of sampling a continuous signal can be converted to a discrete signal, manipulated via a computer program and then converted back into a continuo
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  • ...u have used a good sampling rate, you should be able to reconstruct the CT signal without much fuss.
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  • ...ation is defined by the authors of our book as the fitting of a continuous signal to a set of sample values, and is a commonly used procedure to reconstruct ...tion of the CT signal from the sampled signal approximates the original CT signal better.
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  • Let x(t) be a signal with <math>\chi(\omega)=0</math> when <math>|\omega|<\omega_m</math>. P: A real-valued signal x(t) is known to be uniquely determined by its samples when the sampling fr
    2 KB (340 words) - 17:29, 10 November 2008
  • ...actly, from samples. More so, interpolation is the fitting of a continuous signal to a set of sample values. Interpolation can also be defined as a specific
    1 KB (167 words) - 19:39, 10 November 2008
  • The continuous-time Fourier transform provides us with a representation for signals as linear c ...the complex variable s, it is referred to as the Laplace transform of the signal. The complex variable zs can be written as <math>s=\sigma+j\omega</math>, w
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  • ...rm is used on continuous signal while z transform is used for the discrete signal. The z- transform of a general discrete signal x[n] is defined as
    2 KB (316 words) - 15:23, 3 December 2008
  • #'''Signal Reconstruction Using Interpolation:''' the fitting of a continuous signal to a set of sample values ...nals (CD to MP3 albeit a complicated sampling algorithm, MP3 is less dense signal)
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  • :(c) an ability to determine the response of linear systems to any input signal convolution in the time domain. [1,2,4;a,e,k] :(e) an ability to determine the response of linear systems to any input signal by transformation to the frequency domain, multiplication, and inverse tran
    7 KB (1,017 words) - 10:05, 11 December 2008
  • #'''Signal Reconstruction Using Interpolation:''' the fitting of a continuous signal to a set of sample values ...nals (CD to MP3 albeit a complicated sampling algorithm, MP3 is less dense signal)
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  • ##[[Signal Energy and Power_Old Kiwi]] ##[[Continuous-Time and Discrete-Time_Old Kiwi]]
    4 KB (531 words) - 11:32, 25 July 2008
  • (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 periodic
    4 KB (739 words) - 20:48, 30 July 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).
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  • Note: PM refers to the official course book, Digital Signal Processing, 3rd edition, J.G. Proakis and D.G. Manolakis. * Basic Signals and Signal Properties
    9 KB (1,237 words) - 09:29, 5 October 2009
  • * Signal properties (even/odd, periodicity, power, energy, etc.)
    5 KB (643 words) - 11:55, 6 August 2009
  • ...thcal{F}</math> of {a*x(t)+b*y(t)} will be equal to {a*X(w)+b*Y(w)} if the signal is truly linear. Signal <math>x(t)=1, 0<t\le1; 2, 1<t\le2; 0, else=u(t)+u(t-1)-2u(t-2)</math>
    2 KB (327 words) - 08:33, 8 July 2009
  • '''== Time Shifting Property of Continuous-Time Fourier Series ==''' <br> When a time shift is applied to a periodic signal x(t), the period T of the signal is preserved.<br>
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  • ...the DT Fourier transform look like if the discretization represents the CT signal well?". Should we organize another recitation on that topic?--[[User:Mbou
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  • [[Category:signal processing]] ...frequency spectrum of a signal the faster we sample it. Naturally, if the signal changes much faster than the sampling rate, these changes will not be captu
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  • '''Q:''' What is a digital signal? '''A:''' A signal that can be represented by a sequence of 0's and 1's.
    1 KB (170 words) - 10:07, 23 September 2009
  • ...tions caused by analog circuitry. One area that this can be applied is in signal reconstruction, where a low pass analog filter is used on the output of a d ...ed to relax requirements on analog low pass filter design while decreasing signal distortion.
    5 KB (840 words) - 19:08, 22 September 2009
  • ...s time signal (consisting of infinite number of points) to a discrete time signal (finite points). This process enables the conversion of analog signals to ...period T). This can be achieved by multiplying the given continuous time signal by a train of dirac delta functions separated by the time period T. This c
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  • xc(t)=continuous time signal x[n]=discrete time signal
    1 KB (219 words) - 11:36, 23 September 2009
  • ...ermines the number of pixels the camera uses to represent the "continuous" signal (e.g. a mountain, or your smiling significant other) that your digital came Thus the digital camera '''''samples''''' the continuous signal, with a period <math>T</math> (shutter speed) and "on" for length <math>tau
    6 KB (914 words) - 12:07, 22 October 2009
  • ...e the magnitude of each frequency component's contribution to the original signal. Finally, the Fourier Transform is calculated to express these coefficients ...at is commonly referred to as the "spectrum" of the original discrete-time signal, x[n]. To demonstrate why this is the case, consider the following discrete
    8 KB (1,268 words) - 07:16, 23 September 2009
  • ...s attenuating high frequency portions of the image unless they have a high signal energy (aka, they're significant in the reconstruction and representation o
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  • xc(t)=continuous time signal x[n]=discrete time signal
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  • *[[SignalMetricsFormula|Signal Metrics Definitions and Formulas]] (used in [[ECE301]], [[ECE438]]) **[[CT Fourier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of radial frequency- in
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  • keywords: energy, power, signal '''Signal Metrics Definitions and Formulas'''
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  • Table of Continuous-time (CT) Fourier Transform Pairs and Properties | signal (function of t)
    8 KB (1,130 words) - 11:45, 24 August 2016
  • ...ignals_ECE301S11|Compute the norm of a continuous-time complex exponential signal (practice problem)]] from [[ECE301]] ..._signals_ECE301S11|Compute the norm of a discrete-time complex exponential signal (practice problem)]] from [[ECE301]]
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  • =About the Continuous-time Fourier Transform= ...008mboutin| Example of how to take the Fourier transform of a non-periodic signal]]
    2 KB (262 words) - 12:14, 21 February 2011
  • ...ler's formula to compute the norm of a continuous-time complex exponential signal (practice problem)]] from [[ECE301]] ...Euler's formula to compute the norm of a discrete-time complex exponential signal (practice problem)]] from [[ECE301]]
    2 KB (249 words) - 18:27, 23 February 2015
  • ...ectrical Engineers, the first person that comes to mind when someone says "SIGNAL PROCESSING" is Fourier. *Jean Baptiste Joseph Fourier (1768 - 1830) laid a rock-solid foundation for signal analysis, when he claimed that all (continuously differentiable) signals ca
    10 KB (1,646 words) - 11:26, 18 March 2013
  • We'll start with the 2-dimensional rect(*) signal. Here's the 2-dimensional rect(x,y) function and its CSFT:<br><br>
    8 KB (1,397 words) - 11:23, 18 March 2013
  • ...your concepts of Fourier and Z transforms should be absolutely clear for signal processing (DSP ECE 438).--[[User:Hlalwani|Hersh Lalwani]] 14:55, 11 Decemb ...sforms such as laplace, furiere and z-transform and signals and systems of continuous-time and discrete-time. However, it contains a lot of mathematics skill and some
    14 KB (2,366 words) - 17:32, 21 April 2013
  • As everybody in the class seems to know quite well, the continuous-time signal <math> x(t) = cos(t) </math> is a periodic function with period <math> 2\pi ...pling <math> x(t) </math> every <math>T</math>, we obtain a discrete-time signal <math>f[n]</math>. However, <math>f[n]</math> is not necessarily periodic:
    4 KB (736 words) - 17:25, 23 April 2013
  • ...teral z-Transform. Sampling, quantization, and discrete-time processing of continuous-time signals. Discrete-time nonlinear systems: median-type filters, threshold de <br/>iii. an ability to determine the response of linear systems to any input signal by convolution in the time domain.
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  • <br/><br/>9. Signal detection, signal estimation, cross-correlation functions<br/><br/>
    2 KB (231 words) - 07:20, 4 May 2010
  • [[Category:digital signal processing]] ...hat can be used to describe almost anything in the world be it an electric signal or the stock market. Did you know that our brain picks up different frequen
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  • Note: PM refers to the official course book, Digital Signal Processing, 3rd edition, J.G. Proakis and D.G. Manolakis. Prentice Hall, 19 *Basic Signals and Signal Properties
    9 KB (1,331 words) - 07:15, 29 December 2010
  • ...computation|A collective page to practice computing Fourier series of a CT signal]] ...putation_DT|A collective page to practice computing Fourier series of a DT signal]]
    2 KB (211 words) - 05:39, 26 September 2011
  • Continuous-time Fourier Transform Pairs and Properties | signal (function of t)
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  • [[Category:Fourier series continuous-time]] ...pages contains exercises to practice computing the Fourier series of a CT signal =
    5 KB (797 words) - 09:43, 29 December 2010
  • ...pages contains exercises to practice computing the Fourier series of a DT signal = *Fourier series of a discrete-time signal x[n] periodic with period N
    2 KB (355 words) - 09:44, 29 December 2010
  • =Exercise: Compute the Fourier series coefficients of the following signal:= [[Recommended_exercise_Fourier_series_computation|More exercises on computing continuous-time Fourier series]]
    2 KB (324 words) - 08:08, 15 February 2011
  • ...condition, the sampling frequency must be larger than the twice of maximum signal frequency, in order to avoid the aliasing when sampling. The frequency domain relationship betweeen a signal <math>x[n]</math> and its upsampled version <math>z[n]</math> can be shown
    3 KB (467 words) - 19:52, 20 September 2010
  • ...es, a low-pass filter could be applied to this upsampling so to obtain the signal
    1 KB (220 words) - 16:07, 22 September 2010
  • [[Category:digital signal processing]] <math>\text{ Sample a continuous signal x(t)=sin(}\omega t)\text{ with period of T, }</math>
    2 KB (373 words) - 10:41, 11 November 2011
  • The highest frequency of the continuous signal is <math>f=\frac{\omega}{2\pi}</math>
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  • =Exercise: Compute the Fourier series coefficients of the following periodic signal:= ...ary to state the period in the question, as one can figure it out from the signal itself. </span> --[[User:Mboutin|Mboutin]] 08:15, 29 September 2010 (UTC)
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  • *Fourier series of a continuous-time signal x(t) periodic with period T *Fourier series coefficients of a continuous-time signal x(t) periodic with period T
    2 KB (292 words) - 17:13, 30 September 2010
  • *Fourier series of a continuous-time signal x(t) periodic with period T *Fourier series coefficients of a continuous-time signal x(t) periodic with period T
    1 KB (241 words) - 06:50, 30 September 2010
  • ...transforms one complex-valued function of a real variable into another. In signal processing, the domain of the original function is typically in the time do
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  • Definition: let x[n] be a DT signal with Period N. Then, ...efficients of continuous periodic function x[n]? <br> The DFT of a sampled signal x[n] of length N is directly proportional to the Fourier series coefficient
    19 KB (3,208 words) - 11:23, 30 October 2011
  • [[Category:signal]] keywords:signal energy, exercises
    1 KB (207 words) - 16:04, 25 February 2015
  • [[Category:signal]] =Continuous-Time (Average) Signal Power=
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  • ...ar filtering view of the STFT. Then we obtained a formula to reconstruct a signal from its STFT. This concluded the material on speech processing. We then be
    933 B (122 words) - 09:32, 11 November 2011
  • =About the Multiplication Property of the continuous-time Fourier transform= The multiplication property of the continuous-time Fourier transform can be stated as follows:
    751 B (105 words) - 16:17, 30 November 2010
  • ...[Complex Exponential and Sinusoidal Amplitude Modulation|videos explaining signal modulation]]! ...problems to practice CT convlution, and two problems for practicing basic signal's properties. -pm
    18 KB (2,485 words) - 10:36, 11 November 2011
  • Compute the Magnitude of the following continuous-time signals ...of the result. (This is basically what you are doing in a), but since the signal is real, it is equal to its conjugate.) A quick note though on the symbol <
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  • [[Category:signal]] [[Category:continuous-time signal]]
    4 KB (595 words) - 11:01, 21 April 2015
  • ...\omega\right| > \omega_m </math>. Can one recover the signal x(t) from the signal <math class="inline"> y(t)=x(t) p(t-3) </math>, where ...omega)\right| > \omega_m </math>. Can one recover the signal x(t) from the signal <math class="inline"> y(t)=x(t) p(t-3) </math>, where
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  • *[[SignalMetricsFormula|Signal Metrics Definitions and Formulas]] *[[CT Fourier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml"
    890 B (101 words) - 17:30, 21 April 2013
  • ...olving|Practice Question]] on Computing the Fourier Series continuous-time signal= Obtain the Fourier series the CT signal
    4 KB (594 words) - 12:59, 16 September 2013
  • *[[CT_Fourier_series_practice_problems_list|Problems on continuous-time Fourier series]] *[[CT_Fourier_transform_practice_problems_list|Problems on continuous-time Fourier transform]]
    12 KB (1,768 words) - 10:25, 22 January 2018
  • ...ractice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    1 KB (197 words) - 10:25, 11 November 2011
  • Today we obtained the formula for the Fourier transform of a periodic signal. We found that we cannot compute the Fourier transform of such signals usi We finished the lecture by discussing a few properties of the continuous-time Fourier transform.
    2 KB (215 words) - 14:12, 28 February 2011
  • ...ractice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    2 KB (276 words) - 10:25, 11 November 2011
  • ...ractice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    2 KB (355 words) - 10:26, 11 November 2011
  • ...ractice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    853 B (122 words) - 10:26, 11 November 2011
  • ...ractice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    1 KB (196 words) - 10:26, 11 November 2011
  • Compute the Fourier transform of the continuous-time signal <math>x(t)=e^{-3 |t|}</math>. (Use the definition of the Fourier transform, Compute the Fourier transform of the signal
    4 KB (633 words) - 12:31, 2 March 2011
  • ...irst part of today's lecture, we finished discussing the properties of the continuous-time Fourier transform. We then used these properties to obtain a simple express ...of shifted copies (shifted by <math>2 \pi k</math>, with k integer)of our signal.
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  • = [[:Category:Problem_solving|Practice Question]] on the Properties of the Continuous-time Fourier Transform = Let x(t) be a continuous time signal with Fourier transform <math class="inline">{\mathcal X} (\omega) </math>.
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  • .../span> for the computation of the Fourier transform of the continuous-time signal. Check every step of the computation and remove point for any mistakes. Tak ...r:red"> 15 pts </span> for the computation of the Fourier transform of the signal. Check every step of the computation and remove point for any mistakes. Tak
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  • ...(t). &nbsp;The physiological system being modeled, h(t), will convert this signal into output, y(t). &nbsp;For example, the blood clotting mechanism can be i ...rresponding to adenine, guanine, cytosine, and thymine.) Furthermore, this signal must be broken into distinct genes and decoded. &nbsp;These genes can be ma
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  • The signal <math class="inline"> x(t)= e^{j \pi t }\frac{\sin (\pi t)}{t} </math> is s ...omega \right| > \omega_m </math>. Can one recover the signal x(t) from the signal <math class="inline"> y(t)=x(t) p(t-3) </math>, where
    3 KB (451 words) - 06:40, 1 April 2011
  • [[Category:signal processing]] = [[ECE438|ECE 438]]: Digital Signal Processing with Applications =
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  • [[Category:signal processing]] Note: PM refers to the official course book, Digital Signal Processing, 3rd edition, J.G. Proakis and D.G. Manolakis. Prentice Hall, 19
    9 KB (1,341 words) - 03:52, 31 August 2013
  • ...tal_signal_processing_practice_problems_list|Practice Question on "Digital Signal Processing"]]''' Topic: Continuous-time Fourier transform computation (in terms of frequency f in hertz)
    7 KB (1,302 words) - 09:45, 11 November 2013
  • ...tal_signal_processing_practice_problems_list|Practice Question on "Digital Signal Processing"]]''' Topic: Continuous-time Fourier transform: from omega to f
    7 KB (1,143 words) - 09:44, 11 November 2013
  • ...tal_signal_processing_practice_problems_list|Practice Question on "Digital Signal Processing"]]''' Topic: Continuous-time Fourier transform of a complex exponential
    3 KB (610 words) - 09:47, 11 November 2013
  • ...ture 13, we discussed the possibility of an extra credit project involving signal resampling and filtering. ...p to figure out how to transform this signal into the (higher resolution) signal
    2 KB (243 words) - 06:23, 11 September 2013
  • [[Category:signal processing]] Pick 5 different continuous-time signals x(t) (at least three of which should be band-limited, and at least
    2 KB (320 words) - 03:54, 31 August 2013
  • ...computation|A collective page to practice computing Fourier series of a CT signal]] ...putation_DT|A collective page to practice computing Fourier series of a DT signal]]
    2 KB (212 words) - 05:44, 26 September 2011
  • ...tal_signal_processing_practice_problems_list|Practice Question on "Digital Signal Processing"]]''' Give examples of continuous-time signals that are band-limited. (Justify your claim that they are band-limit
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  • '''Signal''' ...is a function, so when we say a continuous time signal or a discrete time signal we really mean continuous time functions and discrete time functions.
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  • [[Category:signal processing]]
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  • ...tal_signal_processing_practice_problems_list|Practice Question on "Digital Signal Processing"]]''' ...n the exam, you could use the second approach if you were given a table of continuous-time fourier transform in which the Fourier transform of an exponential is given
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  • ...tal_signal_processing_practice_problems_list|Practice Question on "Digital Signal Processing"]]'''
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  • ...tal_signal_processing_practice_problems_list|Practice Question on "Digital Signal Processing"]]'''
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  • [[Category:signal processing]]
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  • ...tal_signal_processing_practice_problems_list|Practice Question on "Digital Signal Processing"]]''' Compute the discrete-space Fourier transform of the following signal:
    3 KB (473 words) - 12:59, 26 November 2013
  • [[Category:Digital Signal Processing]] ...://www.projectrhea.org/learning/practice.php Practice Problems] on Digital Signal Processing
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Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang