(New page: = Lecture 16 Blog, ECE438 Fall 2010, Prof. Boutin = Wednesday September 30, 2010. ---- In Lecture #16, we We also emphasized the need to be able to compute Fourier...) |
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Wednesday September 30, 2010. | Wednesday September 30, 2010. | ||
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| − | In Lecture #16, we | + | In Lecture #16, 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. |
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We also emphasized the need to be able to compute Fourier series, as computing DFTs is essentially the same as computing Fourier series coefficients. | We also emphasized the need to be able to compute Fourier series, as computing DFTs is essentially the same as computing Fourier series coefficients. | ||
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Relevant Links: | Relevant Links: | ||
*[[Student_summary_Discrete_Fourier_transform_ECE438F09|A page about the DFT written by a student]] | *[[Student_summary_Discrete_Fourier_transform_ECE438F09|A page about the DFT written by a student]] | ||
Latest revision as of 15:59, 8 October 2010
Lecture 16 Blog, ECE438 Fall 2010, Prof. Boutin
Wednesday September 30, 2010.
In Lecture #16, we obtained a "practical" formula for reconstructing the DTFT of a finite duration signal from the 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.
We also emphasized the need to be able to compute Fourier series, as computing DFTs is essentially the same as computing Fourier series coefficients.
Relevant Links:
Previous: Lecture 15; Next: Lecture 17
