Composing two Impulse Responses

Question

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.

Answer 1

Yes, that's correct.

The impulse response of a cascade of two systems is the convolution of the individual Impulses responses. Convolution is commutative, so it doesn't matter in which order you convolve.

Impulse responses are ONLY defined for linear time invariant systems, so this will work for systems like equalizers or filters but NOT for things like dynamic processors or limiters.