Dr. Giorgio Casinovi – Publications
Sampling and Ergodic Theorems for Weakly Almost Periodic Signals
G. Casinovi
IEEE Transactions on Information Theory
vol. 55, no. 4, pp. 1883–1897, April 2009
Abstract
The theory of abstract harmonic analysis on commutative groups
is used to prove sampling and ergodic theorems concerning
a particular class of finite-power signals, which are known
as weakly almost periodic. The analysis brings to light
some noteworthy differences between finite-energy and
finite-power signal sampling. It is shown that
the bandwidth of the Fourier transform of a weakly almost
periodic signal is generally larger than the bandwidth of
the power spectrum of the signal. Consequently, the signal
power spectrum by itself does not generally provide enough
information to determine the value of the time-domain Nyquist
rate, that is, the minimum sampling rate necessary for exact
signal reconstruction in the time-domain. On the other hand,
it is also shown that
the minimum sampling rate needed to obtain alias-free spectral
estimates is determined by the bandwidth of the power spectrum
and, consequently, may be lower than the time-domain Nyquist
rate. Finally, the sampling and ergodic theorems established in
this paper are used in an analysis of averaged periodogram
estimates of the power spectrum of a weakly almost periodic
signal. It is shown that the value of the time
shift between consecutive windows may contribute to the
asymptotic bias of the estimates.
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Last revised on January 14, 2014.