# Composing two Impulse Responses

Pardon my layperson understanding. My application is audio design.

What is the correct operation / algorithm to compose two impulse responses (IRa, IRb) into a third impulse response IRc such that it equals the response of running a signal through IRa then IRb?

Am I correct that since IRs represent the response to the delta function, that I can simply convolve IRa by IRb directly? i.e:

IRc[n] = IRa[n] * IRb[n]

Without needing to worry about deconvolving the output of the first IR convolution?

Thank you.