Journal ArticleDOI
Approximation of matrices by Gabor multipliers
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A fast Fourier transform based algorithm which allows to obtain the best approximation of a given time-variant linear system by approximating its matrix (in the Hilbert-Schmidt sense) by a Gabor multiplier, using a given tight Gabor frame.Abstract:
We present a fast Fourier transform based algorithm which allows to obtain the best approximation of a given time-variant linear system by approximating its matrix (in the Hilbert-Schmidt sense) by a Gabor multiplier, using a given tight Gabor frame. We illustrate the approach by approximating the inverse of a slowly time variant filter.read more
Citations
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Modulation Spaces: Looking Back and Ahead
TL;DR: In this paper, the authors provide historical perspectives and background on the motivations which led to the invention of the modulation spaces by the author almost 25 years ago, as well as comments about their role for ongoing research eorts within time-frequency analysis.
Posted Content
Hilbert-Schmidt Operators and Frames - Classification, Approximation by Multipliers and Algorithms
TL;DR: In this article, the authors deal with the connection of frames with the class of Hilbert Schmidt operators and give an easy criteria for operators being in this class using frames, which is the equivalent to the criteria using orthonormal bases.
Journal ArticleDOI
Hilbert–schmidt operators and frames — classification, best approximation by multipliers and algorithms
TL;DR: This paper provides a necessary and sufficient condition for an operator to be Hilbert–Schmidt, based on its action on the elements of a frame, and uses this result to provide a numerically efficient algorithm to find the best approximation of an arbitrary matrix by a so-called frame multiplier.
Journal ArticleDOI
Representation of Operators in the Time-Frequency Domain and Generalized Gabor Multipliers
Monika Dörfler,Bruno Torrésani +1 more
TL;DR: In this paper, a characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor multiplier approximations are discussed.
Journal ArticleDOI
Canonical forms of unconditionally convergent multipliers.
Diana T. Stoeva,Peter Balazs +1 more
TL;DR: It is shown that, under mild conditions, unconditionally convergent multipliers can be transformed by shifting weights between symbol and sequence, into multipliers with symbol and Bessel sequences (called multipliers in canonical form).
References
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Book
Ten lectures on wavelets
TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
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Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.
Journal ArticleDOI
The wavelet transform, time-frequency localization and signal analysis
TL;DR: Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied and the notion of time-frequency localization is made precise, within this framework, by two localization theorems.
Journal ArticleDOI
Banach spaces related to integrable group representations and their atomic decompositions, I
TL;DR: In this article, a general theory of Banach spaces which are invariant under the action of an integrable group representation and give their atomic decompositions with respect to coherent states, i.e., the atoms arise from a single element under the group action.
Journal ArticleDOI
Time-frequency localization operators: a geometric phase space approach
TL;DR: The author defines a set of operators which localize in both time and frequency, similar to but different from the low-pass time-limiting operator, the singular functions of which are the prolate spheroidal wave functions.