Hi, I was wondering if there is any difference between normalize an impulse response in the time or frequency domain, respectively. My first though is yes, because the normalization in the time domain could change the ratio between the frequency components. Simulations in matlab suggest that there is not difference but I am not sure.
Thanks for any advise,
Definitely there is no difference. First of all, you should not worry that normalization in the time domain may change the ratio between frequency components - if you scale your impulse up or down all its frequency components get scaled by exactly the same amount, since the Fourier Transform is a linear operation as so all rules of linear systems theory applies, as Remi Cornwall wrote. One more good news is that when you have normalized your impulse in one of the domains, its energy (the integral of the function squared) is exactly equal in the other domain. The energy of your impulse normalized in the time domain is equal to its energy in the frequency domain. This is what the Parseval's theorem says.
If you do the normalization correct, and if you by normalization mean a constant adjustment, then no, there is no difference.
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