• =Exercise: Compute the Fourier series coefficients of the following signal:= [[Recommended_exercise_Fourier_series_computation|More exercises on computing continuous-time Fourier series]]
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  • ...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
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  • ...es, a low-pass filter could be applied to this upsampling so to obtain the signal
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  • [[Category:digital signal processing]] <math>\text{ Sample a continuous signal x(t)=sin(}\omega t)\text{ with period of T, }</math>
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  • 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
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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
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  • ...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
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  • [[Category:signal]] keywords:signal energy, exercises
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  • [[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
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  • =About the Multiplication Property of the continuous-time Fourier transform= The multiplication property of the continuous-time Fourier transform can be stated as follows:
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  • ...[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
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  • 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]]
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  • ...\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"
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  • ...olving|Practice Question]] on Computing the Fourier Series continuous-time signal= Obtain the Fourier series the CT signal
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  • *[[CT_Fourier_series_practice_problems_list|Problems on continuous-time Fourier series]] *[[CT_Fourier_transform_practice_problems_list|Problems on continuous-time Fourier transform]]
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  • ...ractice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
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  • 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.
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  • ...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
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  • 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
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  • [[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
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  • ...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)
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  • ...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
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  • ...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
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  • [[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]]
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  • ...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:
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  • [[Category:Digital Signal Processing]] ...://www.projectrhea.org/learning/practice.php Practice Problems] on Digital Signal Processing
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  • [[Category:digital signal processing]] [[Category:signal processing]]
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  • = [[ECE]] 538: Digital Signal Processing I = *[[SignalMetricsFormula|Signal Metrics Definitions and Formulas]]
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  • Communication, Networking, Signal and Image Processing (CS) ...that <math class="inline">\mathbf{X}\left(t\right)</math> is a zero-mean, continuous-time, Gaussian white noise process with autocorrelation function <math class="in
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  • Communication, Networking, Signal and Image Processing (CS)
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  • Communication, Networking, Signal and Image Processing (CS)
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  • Communication, Networking, Signal and Image Processing (CS) Let <math class="inline">\mathbf{X}\left(t\right)</math> be a real continuous-time Gaussian random process. Show that its probabilistic behavior is completely
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  • Communication, Networking, Signal and Image Processing (CS) ...0"><span style="font-size: 19px;"><math>\color{blue} \text{Show that if a continuous-time Gaussian random process } \mathbf{X}(t) \text{ is wide-sense stationary, it
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  • Communication, Networking, Signal and Image Processing (CS) \text{Let } F(\mu,\nu) \text{ be the continuous-time Fourier transform of } f(x,y) \text{ given by}
    4 KB (665 words) - 10:25, 13 September 2013
  • Communication, Networking, Signal and Image Processing (CS) ...000"><span style="font-size: 19px;"><math>\color{blue}\text{Show that if a continuous-time Gaussian random process } \mathbf{X}(t) \text{ is wide-sense stationary, it
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  • Communication, Networking, Signal and Image Processing (CS) \text{Let } F(\mu,\nu) \text{ be the continuous-time Fourier transform of } f(x,y) \text{ given by}
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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"
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  • To measure the worst case time delay from accelerometer signal input to orientation angle output at a macro scale (ie not by counting asse ...S. Smith, "DSP Software," ''The Scientist and Engineer's Guide to Digital Signal Processing''. <http://www.dspguide.com/ch4.htm>
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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"
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  • ...) = e^{-2}</math> at n=2, and so on. But because we have a constant input signal that effectively serves as a delta function at each time step, another impu ''<center>time-shifted continuous-time impulse responses due to a step function. (theoretically there should be an
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  • ...domain. It’s the output of In a LTI system when presented with a impulse signal input δ(t). In a LTI systems, impulse response is also equivalent to green
    2 KB (322 words) - 23:38, 10 March 2013
  • ...hat the mean of the output random signal is equal to the mean of the input signal multiplied by the frequency response of the system evaluated at f=0. We als Note that we are now focusing only on continuous-time random processes for lack of time.
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  • ::↳ Eigen-Signal Analysis and Examples ...T is for continuous time signals. Let <math>x(n)</math> be a discrete time signal. Then, its DTFT, <math>X(e^{j\omega})</math> is given by <br/>
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  • [[Category:digital signal processing]] [[Category:signal processing]]
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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"
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  • [[Category:signal processing]] ...in terms of <math>\omega</math>, which you have seen in [[ECE301]], to the continuous-time Fourier transform in terms of f. We then saw a few important properties of
    3 KB (505 words) - 06:56, 2 September 2013
  • *[[Audio_Signal_Filtering|Audio Signal Filtering]]
    3 KB (389 words) - 18:10, 23 February 2015
  • on continuous-time Fourier transform ==Collectively solved problems on continuous-time Fourier transform==
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  • on continuous-time Fourier series ==Collectively solved problems on continuous-time Fourier series==
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  • ...x(t) be a continuous-time signal and let y[n]=x(nT) be a sampling of that signal with period T>0. We would like to interpolate the samples (i.e., "connect t ...imited interpolation of the samples (i.e., an expression for a continuous signal z(t) in terms of the samples y[n]). (Do not simply write down the formula;
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  • [[Category:signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''
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  • [[Category:signal processing]] ''' [[ECE438| ECE438: Digital Signal Processing with Applications]]'''
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  • [[Category:signal processing]] *[[2D_rect|2D rect signal]]
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  • [[Category:signal processing]] *[[2D_rect|2D rect signal]]
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  • Communication, Networking, Signal and Image Processing (CS)
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  • <font size="4">Communication, Networking, Signal and Image Processing (CS)</font>
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  • ** Be able to calculate the Fourier series coefficients of a period CT signal (DT Fourier series will NOT be on the exam). (3.28a(subparts abc), 3.22, 3. ...the frequency response of a system, find the FS coefficients of the output signal. (3.13, 3.14, Quiz 3)
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  • =Lab Wiki: [[2014_Fall_ECE_438_Boutin|ECE 438: Digital Signal Processing With Applications]], Fall 2014=
    2 KB (380 words) - 08:18, 2 December 2014
  • [[Category:digital signal processing]] [[Category:signal processing]]
    9 KB (1,320 words) - 04:46, 11 September 2014
  • [[Category:signal processing]] ...in terms of <math>\omega</math>, which you have seen in [[ECE301]], to the continuous-time Fourier transform in terms of f. We then saw a few important properties of
    3 KB (393 words) - 06:37, 27 August 2014
  • [[Category:signal processing]] ...led'. But this process is a little different from sampling. The continuous signal will become discrete after sampling while it will still be continuous after
    5 KB (768 words) - 18:51, 16 March 2015
  • ...nderstand the relation between comb vs original signal and rep vs original signal.
    7 KB (1,226 words) - 05:30, 15 October 2014
  • ...x(t) be a continuous-time signal and let y[n]=x(nT) be a sampling of that signal with period T>0. We would like to interpolate the samples (i.e., "connect t ...imited interpolation of the samples (i.e., an expression for a continuous signal z(t) in terms of the samples y[n]). (Do not simply write down the formula;
    3 KB (462 words) - 09:43, 18 September 2014
  • ...x(t) be a continuous-time signal and let y[n]=x(nT) be a sampling of that signal with period T>0. We would like to interpolate the samples (i.e., "connect t ...imited interpolation of the samples (i.e., an expression for a continuous signal z(t) in terms of the samples y[n]). (Do not simply write down the formula;
    7 KB (1,178 words) - 20:16, 18 December 2014
  • [[Category:signal processing]] The discrete time fourier transform (DTFT) of a finite energy aperiodic signal x[n] can be given by the equation listed below. IT is a representation in t
    5 KB (862 words) - 20:02, 16 March 2015
  • [[Category:signal processing]] ...g this cosine with period T (frequency <math>f_{s}=1/T</math>, the sampled signal <math>x[n]</math> can be written as <math>x[n]=cos(\frac{2 \pi f n}{T})</ma
    5 KB (801 words) - 20:04, 16 March 2015
  • [[Category:signal processing]] ...nly be reconstructed perfectly from its sampling <math>x_s(t)</math>if the continuous-time Fourier Transform (CTFT) of <math>x(t)</math> is zero for all magnitudes of
    10 KB (1,650 words) - 19:04, 16 March 2015
  • [[Category:signal processing]] ...cy domain view of the relationship between a signal and a sampling of that signal
    4 KB (732 words) - 19:07, 16 March 2015
  • [[Category:signal processing]] ...cy domain view of the relationship between a signal and a sampling of that signal
    5 KB (852 words) - 09:58, 14 March 2015
  • ...cy domain view of the relationship between a signal and a sampling of that signal </font> ...ship between a signal, and a sampling of that signal. Essentially, given a signal x(t), we are going to take a look at the similarities and differences in X(
    4 KB (599 words) - 09:58, 14 March 2015
  • #Derivation of DTFT&nbsp;of downsampled signal<br> ...ure provides definition of downsampling, derives DTFT of&nbsp; downsampled signal and demonstrates it in a frequency domain. Also, it explains process of dec
    7 KB (1,035 words) - 19:07, 16 March 2015
  • ...to eliminate the possibility of aliasing and distorting the reconstructed signal. Begin with x(t) as a continuous time signal with <math>x_1[n]= x(T_1*n)</math> being its discrete time sampling.
    4 KB (566 words) - 09:59, 14 March 2015
  • ...cy domain view of the relationship between a signal and a sampling of that signal </font> ...f original signal x(t), sampled signal&nbsp; x<sub>s</sub>(t) and discrete signal x<sub>d</sub>[n]. Graphs in frequency domain&nbsp; help to understand this
    4 KB (621 words) - 05:40, 15 October 2014
  • =Lab Wiki: [[2015_Fall_ECE_438_Boutin|ECE 438: Digital Signal Processing With Applications]], Fall 2015=
    2 KB (303 words) - 13:45, 5 October 2015
  • [[Category:digital signal processing]] [[Category:signal processing]]
    10 KB (1,356 words) - 13:19, 19 October 2015
  • =Lab Wiki: [[2015_Spring_ECE_438_Ersoy|ECE 438: Digital Signal Processing With Applications]], Spring 2015=
    2 KB (384 words) - 11:44, 21 April 2015

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Alumni Liaison

has a message for current ECE438 students.

Sean Hu, ECE PhD 2009