Latest revision as of 14:57, 8 October 2010

Lecture 15 Blog, ECE438 Fall 2010, Prof. Boutin

Monday September 28, 2010.

In Lecture #15, we recalled that, before computing the "DFT of discrete-time signal"(*see note below), one first needs to truncate the signal. Subsequently, one needs to repeat the resulting finite duration signal in order to create a periodic DT signal. The DFT of that periodic signal then corresponds to a sampling of the DTFT of the truncated signal.

We discussed the artifacts created by signal truncation (leakage) and the problems created by sampling the DTFT (the "picket fence effect"). To illustrate the leakage effect, we looked at the Fourier transform of a window function.

Note: Technically, the DFT is only defined for periodic signals.

Previous: Lecture 14; Next: Lecture 16

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 Monday September 28, 2010.
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-In Lecture #15, we obtained a "practical" formula for reconstructing the DTFT of a finite duration signal from the [[Discrete Fourier Transform|DFT]] of its periodic repetition. The formula was observed to hold whenever the periodic repetition has a period that is at least as long as the signal duration. We finished the lecture by introducing a matrix equation to represent the transformation from a finite duration signal to the DFT.
+In Lecture #15, we recalled that, before computing the "DFT of discrete-time signal"(*see note below), one first needs to truncate the signal. Subsequently, one needs to repeat the resulting finite duration signal in order to create a periodic DT signal. The DFT of that periodic signal then corresponds to a sampling of the DTFT of the truncated signal.
+We discussed the artifacts created by signal truncation (leakage) and the problems created by sampling the DTFT (the "picket fence effect"). To illustrate the leakage effect, we [[DTFT_Window_Function|looked at the Fourier transform of a window function]].
-Relevant Links:
+*Note: Technically, the DFT is only defined for periodic signals.
-*[[Student_summary_Discrete_Fourier_transform_ECE438F09|A page about the DFT written by a student]]
-*[[Notes_on_Discrete_Fourier_Transform|My Fall 2009 Notes typed by a student]]
 Previous: [[Lecture14ECE438F10|Lecture 14]]; Next: [[Lecture16ECE438F10|Lecture 16]]

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Latest revision as of 14:57, 8 October 2010

Lecture 15 Blog, ECE438 Fall 2010, Prof. Boutin

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