On discrete Fourier analysis of amplitude and phase modulated signals

Waldemar Popiński. "On discrete Fourier analysis of amplitude and phase modulated signals." Applicationes Mathematicae 39.1 (2012): 57-69. <http://eudml.org/doc/280081>.

@article{WaldemarPopiński2012,
abstract = {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,...,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.},
author = {Waldemar Popiński},
journal = {Applicationes Mathematicae},
keywords = {discrete Fourier transform; finite duration signal; amplitude modulation; phase modulation; spectral analysis of time series},
language = {eng},
number = {1},
pages = {57-69},
title = {On discrete Fourier analysis of amplitude and phase modulated signals},
url = {http://eudml.org/doc/280081},
volume = {39},
year = {2012},
}

TY - JOUR
AU - Waldemar Popiński
TI - On discrete Fourier analysis of amplitude and phase modulated signals
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 1
SP - 57
EP - 69
AB - 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,...,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.
LA - eng
KW - discrete Fourier transform; finite duration signal; amplitude modulation; phase modulation; spectral analysis of time series
UR - http://eudml.org/doc/280081
ER -