I am trying to compare signals in the spectrum domain. The signals have a different number of samples, N samples of signal1 and M samples of signal2. To compare the powers, I am doing an FFT of N samples for signal1 and an FFT of M samples for signal2. To compare both signals, I am dividing the result by N and M respectively to compensate for the FFT process gain.
However, if I zero pad both signals to the same number of samples, should I still divide by N and M or divide by the new FFT size?
On one hand, zero padding is not adding information, so my intuition told me I should still divide by N and M. On the other hand, in all the literature I have found I should divide by the size of the FFT.