How to convolve impulses in engineering?

[DWill]

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!

 

[fresh_42]

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]

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
$\delta(\omega-\omega_0) \ast \delta(\omega-\omega_1) = \delta(\omega-\omega_0-\omega_1)$