[图书][B] Time-frequency and time-scale methods: adaptive decompositions, uncertainty principles, and sampling
Developed in this book are several deep connections between time-frequency
(Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful …
(Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful …
System-time entanglement in a discrete-time model
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 …
the evolving system and a reference quantum clock system. A quantum circuit for the model …
Jones index theory for Hilbert C∗-bimodules and its equivalence with conjugation theory
T Kajiwara, C Pinzari, Y Watatani - Journal of Functional Analysis, 2004 - Elsevier
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 …
bi-Hilbertian structure, based on a Pimsner–Popa-type inequality. The right index of X can …
History states of systems and operators
A Boette, R Rossignoli - Physical Review A, 2018 - APS
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 …
arise for a quantum reference clock of finite dimension and lead to a unitary evolution of …
Applied and Numerical Harmonic Analysis
JJ Benedetto - (No Title), 2007 - Springer
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 …
and engineering with many exciting applications in a variety of different fields. Introduced in …
A Sparse Algorithm for Computing the DFT Using Its Real Eigenvectors
Direct computation of the discrete Fourier transform (DFT) and its FFT computational
algorithms requires multiplication (and addition) of complex numbers. Complex number …
algorithms requires multiplication (and addition) of complex numbers. Complex number …
An entropy-based uncertainty principle for a locally compact abelian group
M Özaydin, T Przebinda - Journal of Functional Analysis, 2004 - Elsevier
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 …
Functional Analysis 215 (2004) 241–252 An entropy-based uncertainty principle for a locally …
[PDF][PDF] The Donoho-Stark uncertainty principle for a finite abelian group.
E Matusiak, M Özaydin, T Przebinda - Acta Mathematica Universitatis …, 2004 - eudml.org
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 …
Donoho and Stark gave an elementary proof that the product of the cardinality of the support …
On computing the discrete Hirschman transform
D Xue, LS DeBrunner… - IEEE Transactions on …, 2020 - ieeexplore.ieee.org
The Discrete Hirschman Transform (DHT) is a generalization of the entropy-based
Hirschman Transform that canonically represents digital signals with sparse basis functions …
Hirschman Transform that canonically represents digital signals with sparse basis functions …
An algorithm to reduce the complexity required to convolve finite length sequences using the Hirschman optimal transform (HOT)
V DeBrunner, E Matusiak - 2003 IEEE International …, 2003 - ieeexplore.ieee.org
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 …
length that is more efficient than its FFT-based competitor. In particular, we present a method …