I want to derive a real audio signal from an arbitrary even magnitude spectrum.
The phase spectrum affects the values of the signal in the time domain; for example, a phase of 0 for all frequencies amounts to summing cosines in the time domain, which will result in a large peak at t = 0. I want to minimize the absolute values of the signal in the time domain without scaling the magnitude spectrum
I want this so that the audio signal can be multiplied by the largest scalar value possible without clipping. Is there a way to compute the phase spectrum that will do that? If there is a stupidly simply solution, I apologize in advance.