On discrete Fourier analysis of amplitude and phase modulated signals
In this work the problem of characterization of the Discrete Fourier Transform (DFT) spectrum of an original complex-valued signal $o_t$, $t=0,1,\dots,n-1$, modulated by random fluctuations of its amplitude and/or phase is investigated. It is assumed that the amplitude and/or phase of the signal at discrete times of observation are distorted by realizations of uncorrelated random variables or randomly permuted sequences of complex numbers. We derive the expected values and bounds on the variances of such distorted signal DFT spectra. It is shown that the modulation considered in general entails changes in the amplitude and/or phase of the DFT spectra expected values, which together with imposed random deviations with finite variances can vary the amplitudes of peaks existing in the original signal spectrum, and consequently similarity to the original signal spectrum can be significantly blurred.