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Convolution theorem in Section 8.4 not correct #11

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spors opened this issue Jan 21, 2016 · 1 comment
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Convolution theorem in Section 8.4 not correct #11

spors opened this issue Jan 21, 2016 · 1 comment

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@spors
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spors commented Jan 21, 2016

The convolution theorem in Section 8.4 is not correct. Multiplication of the DFTs of two signals results in the periodic/circular convolution of the two signals. This is why zero-padding is required when one aims at the linear convolution in order to compute the output of a linear-time invariant system. You fill find this in amost any good textbook on DSP or since you also like Jupyter notebooks http://nbviewer.jupyter.org/github/spatialaudio/digital-signal-processing-lecture/blob/master/nonrecursive_filters/fast_convolution.ipynb.

@AllenDowney
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At this point in the book I have not yet distinguished linear and circular convolution because the examples haven't required it. It comes up later, although I don't use the terms. I will consider adding them. Thanks!

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