I would like to reduce the noise in my psd. Given a signal in time u, that has a length of 80001, and decided the length of my window W_len and the fs=1000. I performed this pwelch
[Swelch, fwelch] = pwelch(u, hanning(W_len), W_len*0.5, 4000, 1000,'onesided' )
The problem is that the integral of this psd is different from the original. Is it possible to obtain the same integral with the pwelch?
Finally, I am struggling to find the equation involved in the pwelch. Does it use the correlation theorem, doing |fft(u)|.^2 ???