Lecture 26 Blog, ECE438 Fall 2010, Prof. Boutin
Monday October 25, 2010.
We looked at the output of a DT system using the DFT. The main result we presented is quite simple: the DFT of the ouput is the product of the DFT of the input, and the DFT of the unit impulse response of the system:
$ Y_N[k]=X_N[k] H_N[k], \text{ for all }k\in {\mathbb Z} $
However, our discussion was complicated by the fact that, technically, the DFT is defined for periodic signals only (thus not for finite duration signals), while in application the input is typically of finite duration. We also had to worry about the fact that the input, the unit impulse response, and the output have different durations, and so we need to make sure to use the N-point DFT, where N is at least as long as x[n], h[n], and y[n].
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