Developed in this book are several deep connections between time-frequency
(Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful …

We present a model of discrete quantum evolution based on quantum correlations between
the evolving system and a reference quantum clock system. A quantum circuit for the model …

We introduce the notion of finite right (or left) numerical index on a C∗-bimodule AXB with a
bi-Hilbertian structure, based on a Pimsner–Popa-type inequality. The right index of X can …

We discuss some fundamental properties of discrete system-time history states. Such states
arise for a quantum reference clock of finite dimension and lead to a unitary evolution of …

Frame theory is nowadays a fundamental research area in mathematics, computer science,
and engineering with many exciting applications in a variety of different fields. Introduced in …

Direct computation of the discrete Fourier transform (DFT) and its FFT computational
algorithms requires multiplication (and addition) of complex numbers. Complex number …

An entropy-based uncertainty principle for a locally compact abelian group Page 1 Journal of
Functional Analysis 215 (2004) 241–252 An entropy-based uncertainty principle for a locally …

Let A be a finite cyclic group and let f be a non-zero complex valued function defined on A.
Donoho and Stark gave an elementary proof that the product of the cardinality of the support …

The Discrete Hirschman Transform (DHT) is a generalization of the entropy-based
Hirschman Transform that canonically represents digital signals with sparse basis functions …

We develop an algorithm suitable for convolving two finite length sequences of uneven
length that is more efficient than its FFT-based competitor. In particular, we present a method …