if we pad any signal with enough zeros we can get the same result as linear convolution whilst using the fft function we compute circular convolution. Why?

  • 2
    $\begingroup$ It's usually thought of as the other way around. The windowing you choose impacts a trade-off between frequency and time resolution regarding non-stationary data. You may have to prioritize. $\endgroup$ – hotpaw2 Nov 1 '13 at 18:03
  • $\begingroup$ can you explain more plz? $\endgroup$ – fransisco Nov 1 '13 at 20:56
  • $\begingroup$ Just curious, in practical implementations, is there a relationship between the time resolution and frequency resolution? @hotpaw? $\endgroup$ – meta_warrior Nov 4 '13 at 0:14

Hint: try computing the linear convolution of $~[1\quad 1\quad 1]~$ and $~[0\quad 1 \quad 1]~$ by hand and the circular convolution of the zero-padded versions $~[1\quad 1\quad 1 \quad 0\quad 0\quad 0]~$ and $~[0\quad 1 \quad 1\quad 0\quad 0\quad 0]~$ also by hand (or via FFTs if you are desperate enough).

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  • $\begingroup$ I know how to do linear convolution but what is circular convolution or how can i compute circular convolution using fft $\endgroup$ – fransisco Nov 7 '13 at 18:48

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