Foundations Of Time Frequency Analysis

By Christina Gloeckner. 2016

1,220 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ed362097b434938359a7d06c4292212a7f59938c

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Citations in the corpus

Window-Dependent Bases for Efficient Representations of the Stockwell Transform (2014, methodology): “One of the standard tool is the short-time Fourier transform Loosely speaking, taking the short-time Fourier transform of a signal f at a certain time b is like taking the Fourier transform of the signal f cut by a window function ϕ centered in b , see for example [13], [17].”
A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction (2015, background): “The atoms { g k } k ∈ Z satisfy the Littlewood-Paley condition (35) according to A popular function g ∈ L 1 ( R ) ∩ L 2 ( R ) satisfying (36) is the Gaussian function [74].”
α-modulation spaces (I) scaling, embedding and algebraic properties (2014, background): “Gröchenig’s book [12] systematically discussed the theory of time-frequency analysis and modulation spaces.”
The Zak transform and the structure of spaces invariant by the action of an LCA group (2014, methodology): “Closed spaces that are invariant under a certain kind of unitary operators are of particular importance in several areas of Harmonic Analysis such as wavelets, spline systems, Gabor systems and approximation theory [1, 19, 24, 30, 33].”
Reproducing formulas for generalized translation invariant systems on locally compact abelian groups (2014, methodology): “We refer the reader to the classical texts [12,14,27] and the recent book [38] for introductions to the specific cases of Gabor, wavelet, shearlet and wave packet analysis.”
Images of function and distribution spaces under the Bargmann transform (2014, methodology): “mit any weight function, and show that these spaces are quasiBanach spaces, and thereby complete. In the last part of the section we analyze the test function space SC(Rd), introduced by Gröchenig in [15], and compare this space with H0,♭1(R d) and H ♭1(R d). The following results identify the space”
The Faber–Krahn inequality for the short-time Fourier transform (2021, methodology): “Let S (cid:48) ( R ) be the space of temperate distributions and, for p ≥ 1, consider the subspace (called modulation space in the literature [33]) In fact, the deﬁnition of STFT (with Gaussian or more generally Schwartz window) and the Bargmann transform B extend (in an obvious way) to injective…”
Functions operating on modulation spaces and nonlinear dispersive equations (2014, background): “Subsequently, in a joint work with K. Gröchenig, the basic theory of these function spaces were established in [6, 7].”