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In signal processing systems, aliasing is normally treated as a disturbing signal. That motivates the need for effective analog, optical and digital anti-aliasing filters. However, aliasing conveys also valuable information on the signal above the Nyquist ...
Sampling theory has prospered extensively in the last century. The elegant mathematics and the vast number of applications are the reasons for its popularity. The applications involved in this thesis are in signal processing and communications and call out ...
"Random spikes" belong to the common language used by engineers, physicists and biologists to describe events associated with time records, locations in space, or more generally, space-time events. Indeed, data and signals consisting of, or structured by, ...
Sampling theory has experienced a strong research revival over the past decade, which led to a generalization of Shannon's original theory and development of more advanced formulations with immediate relevance to signal processing and communications. For e ...
Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of the unifying role and their successes in applications. Filter banks, which lie at the heart of wavelet-based algorithms, have become st ...
Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform ...
Institute of Electrical and Electronics Engineers2002
Many communication systems are {\em bandwidth-expanding}: the transmitted signal occupies a bandwidth larger than the {\em symbol rate}. The sampling theorems of Kotelnikov, Shannon, Nyquist et al. shows that in order to represent a bandlimited signal, it ...
Recently a sampling theorem for a certain class of signals with finite rate of innovation (which includes for example stream of Diracs) has been developed. In essence, such non band-limited signals can be sampled at or above the rate of innovation. In the ...
We consider the problem of reconstructing a multidimensional and multivariate function ƒ: ℜm \rightarrow ℜn from the discretely and irregularly sampled responses of q linear shift-invariant filters. Unlike traditional approaches which r ...