1
$\begingroup$

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?

$\endgroup$
  • 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? $\endgroup$ – freak_warrior Nov 4 '13 at 0:14
2
$\begingroup$

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).

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.