While considering an input to be periodic of Period N, can the impulse response not be periodic of period greater than N ? If it can be, how can one compute it’s convolution?


Circular convolution assumes that all signals ($x[n]$, $h[n]$ and $y[n]$) are periodic in the same integer $L$. When any of the signals are shorther than $L$ then they are padded with enough zeros to make them periodic with $L$. When $x$ or $h$ has a period larger than $L$ then there will be aliasing in the computed output $y[n]$ which is still periodic with $L$.

  • $\begingroup$ can you explain a little bit on the aliasing part please $\endgroup$ Oct 22 '17 at 16:43
  • $\begingroup$ I mean would the alias be having a period longer than L or shorter ? @Fat32 $\endgroup$ Oct 22 '17 at 16:52
  • $\begingroup$ result of circular convolution will always be periodic in L, whether there is aliasing or not. $\endgroup$
    – Fat32
    Oct 22 '17 at 17:21
  • $\begingroup$ I can understand that, but let's just say that we have a sine wave, periodic of period N, let the impulse response be an impulse as well, If I am to convolve the two for a period L, where L< N , I cannot understand how the output y[n] be an alias because it is not periodic of period N. $\endgroup$ Oct 22 '17 at 17:31

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