As the question states, is it possible to predict the peak value of a time-domain signal given its frequency-domain spectrum?
Since the time-domain signal is just the sum of the individual sinusoids making up the frequency domain spectrum (i.e. inverse Fourier transform), I have been reading some answers on estimating the peak amplitude of a sum of sinusoids:
However, none of these questions really precisely ask the question I am asking (i.e. no specific reference to FT), and I wonder if there is some "magic" in the theory of Fourier transforms that allows this to be done. Note that I realize the trivial answer here is: take the inverse FT and find the peak! I also realize that it can be done analytically for certain functions (e.g. square wave, delta spike, etc).
To add a twist, I would also ask if there is a way to predict the peak value of the multiplication of two frequency-domain spectra? In this case, I wonder if there's any "magic" in convolution theory that would allow this to be done. If you convolve two time-domain signals, is there a way to predict the peak value of the convolved signal? This is equivalent to asking if you can find the peak time-domain value of the multiplication of two spectra.
Any info is appreciated.