# Convolution of Impulses

## Main Question or Discussion Point

Hi guys,

I am just having a bit of difficulty figuring out how to do convolution of impulses. Suppose I have a function consisting of impulses located at -2ω0, 0, and +2ω0 (in frequency domain) with some arbitrary amplitude A. I want to convolve this function with another function consisting of two impulses located at -1ω0 and +1ω0 with some other arbitrary amplitude B.

I'm mainly confused because I'm not sure how the multiplication of two impulses would work.

Can anyone show me how this is done?

Thank you very much!

## Answers and Replies

fresh_42
Mentor
The convolution of periodic functions ##f,g## with period ##T## is defined as ##(f\ast g)(t)=\int_a^{a+T}f(\tau)g(t-\tau)\,d\tau ## so the only problem is to describe your impulses by e.g. a sine function.

jasonRF
Science Advisor
Gold Member
It ia common for engineers to use the word "impulses" for delta functions. If this is what the OP is referring to, then the convolution of impulses follows the rule
## \delta(\omega-\omega_0) \ast \delta(\omega-\omega_1) = \delta(\omega-\omega_0-\omega_1)
##