Distribution theory and transform analysis: an introduction to generalized functions, with applications
Higher-order cyclostationarity properties of sampled time-series
Signal Processing
IEEE Spectrum
Cyclostationarity: half a century of research
Signal Processing
On spatial aliasing in microphone arrays
IEEE Transactions on Signal Processing
Discrete-time estimation of second-order statistics of generalized almost-cyclostationary processes
IEEE Transactions on Signal Processing
Second-order analysis of improper complex random vectors and processes
IEEE Transactions on Signal Processing
The estimation of time delay and Doppler stretch of widebandsignals
IEEE Transactions on Signal Processing
Uncertainty in measurements on spectrally correlated stochastic processes
IEEE Transactions on Information Theory
Estimation of Second-Order Cross-Moments of Generalized Almost-Cyclostationary Processes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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The paper deals with Doppler-stretched wide-band signals occurring in mobile communications and in radar/sonar problems in the presence of moving targets in the case of constant relative radial speeds. Loeve bifrequency spectrum and cross-spectrum are used to characterize in the spectral domain the received signal and to jointly characterize the transmitted and received signals. It is shown that, even if both the transmitted and received signals are singularly almost-cyclostationary (ACS), they are not jointly ACS but, rather, jointly spectrally correlated. The problem of uniformly sampling these nonstationary signals is addressed. It is shown that, unlike the case of the wide-sense stationary signals, several kind of aliasing effects occur for the various spectral (cross-)statistical functions used to characterize these signals. Lower bounds on the sampling frequency are derived to avoid these aliasing effects.