# When does the convolution of $2$ signals equals zero?

For example, how can I determine if the convolution of $x(t)$ with $y(t)$ is equal to $0$?

• Circular or linear convolution? And if linear, do you care about the initial/ending transients being zero or not? – hotpaw2 Apr 27 '16 at 4:38
• linear convolution. I just need an example to understand under what circumstances I can end with 0 after convolving to signals together. The output should be zero. thanks! – Carlos M. Navarro Apr 27 '16 at 4:41
• Consider a rectangular pulse rect$\left(\frac tT\right)$ of duration $T$ and a DC-free periodic signal of period $T$. For any delay, the convolution integral evaluates to $T$ times the average value of the periodic signal, that is, the convolution integral has value $0$. – Dilip Sarwate Apr 30 '16 at 14:07

• For periodic signals with no coinciding non-zero harmonics, e.g, $\cos t$ and $\cos \pi t$, there is also the question of whether the convolution integral converges. – Dilip Sarwate Apr 30 '16 at 14:11