Suppose $x[n]$ and $y[n]$ are two nonzero signals(i.e., $x[n] \neq 0$ for at least one value of n and similarly for $y[n]$).Can the convolution between $x[n]$ and $y[n]$ result in an identically zero signal? In other words, is it possible that $\displaystyle\sum_{k = -\infty}^{k = +\infty}x[k]y[n-k] = 0$ for all n.


1 Answer 1


Yes, for example let


for all $k$ and

$$y[k] = \begin{cases}1 & k=0\\-1 & k=1\\0 & otherwise \end{cases}$$

It is easy to see that in case of a convolution, the result will be zero for all values of $n$.

  • 4
    $\begingroup$ It is worth noting that this result only holds if the signal $x[k]$ has infinite length. In practice you will see non-zero convolution tails. $\endgroup$
    – nispio
    Oct 24, 2013 at 22:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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