On Discrete Fourier Spectrum of Randomly Modulated Signals

In this work the problem of characterization of Discrete Fourier Transform (DFT) spectrum of an original complex-valued signal modulated by random fluctuations of amplitude and phase is investigated. It is assumed that the amplitude and phase of signal values at discrete time moments of observations are distorted by adding realizations of independent and identically distributed random variables. The obtained results of theoretical analysis of such distorted signal spectra show that only in the case of amplitude modulation the DFT spectrum of the modulated bounded signal can be similar to the original signal spectrum, although there occur random deviations. On the other hand, if phase modulation is present, then the DFT spectrum of the modulated bounded signal not only shows random deviations but also amplitudes of peaks existing in the original spectrum are diminished, and consequently similarity to the original signal spectrum can be significantly blurred.