# Impulse response time period in circular convolution

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?

## 1 Answer

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 $L$.

• can you explain a little bit on the aliasing part please – Syed Mohammad Asjad Oct 22 '17 at 16:43
• I mean would the alias be having a period longer than L or shorter ? @Fat32 – Syed Mohammad Asjad Oct 22 '17 at 16:52
• result of circular convolution will always be periodic in L, whether there is aliasing or not. – Fat32 Oct 22 '17 at 17:21
• 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. – Syed Mohammad Asjad Oct 22 '17 at 17:31