Statistical view on phase and magnitude information in signal processing

In this work the problem of reconstruction of an original complex-valued signal ot, t = 0, 1,...,n - 1, from its Discrete Fourier Transform (DFT) spectrum corrupted by random fluctuations of magnitude and/or phase is investigated. It is assumed that the magnitude and/or phase of discrete spectrum values are distorted by realizations of uncorrelated random variables. The obtained results of analysis of signal reconstruction from such distorted DFT spectra concern derivation of the expected values and bounds on variances of the reconstructed signal at the observation moments. It is shown that the considered random distortions in general entail change in magnitude and/or phase of the reconstructed signal expected values, which together with imposed random deviations with finite variances can blur the similarity to the original signal. The effect of analogous random amplitude and/or phase distortions of a complex valued time domain signal on band pass filtration of distorted signal is also investigated.

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).