Gabor-frame-based Gaussian packet migration

2014 ◽  
Vol 62 (6) ◽  
pp. 1432-1452 ◽  
Author(s):  
Yu Geng ◽  
Ru-Shan Wu ◽  
Jinghuai Gao
Keyword(s):  
Gabor Frame ◽  
Gaussian Packet

scholarly journals Invertibility of the Gabor frame operator on the Wiener amalgam space

2008 ◽  
Vol 153 (2) ◽  
pp. 212-224 ◽  
Author(s):  
Ilya A. Krishtal ◽  
Kasso A. Okoudjou
Keyword(s):  
Gabor Frame ◽  
Frame Operator ◽  
Wiener Amalgam Space

scholarly journals Hilbert space valued Gabor frames in weighted amalgam spaces

2019 ◽  
Vol 10 (4) ◽  
pp. 377-394
Author(s):  
Anirudha Poria ◽  
Jitendriya Swain
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Gabor Frame ◽  
Window Function ◽  
Gabor Frames ◽  
Frame Operator ◽  
Wiener Amalgam Space ◽  
Amalgam Spaces ◽  
Special Case

AbstractLet {\mathbb{H}} be a separable Hilbert space. In this paper, we establish a generalization of Walnut’s representation and Janssen’s representation of the {\mathbb{H}}-valued Gabor frame operator on {\mathbb{H}}-valued weighted amalgam spaces {W_{\mathbb{H}}(L^{p},L^{q}_{v})}, {1\leq p,q\leq\infty}. Also, we show that the frame operator is invertible on {W_{\mathbb{H}}(L^{p},L^{q}_{v})}, {1\leq p,q\leq\infty}, if the window function is in the Wiener amalgam space {W_{\mathbb{H}}(L^{\infty},L^{1}_{w})}. Further, we obtain the Walnut representation and invertibility of the frame operator corresponding to Gabor superframes and multi-window Gabor frames on {W_{\mathbb{H}}(L^{p},L^{q}_{v})}, {1\leq p,q\leq\infty}, as a special case by choosing the appropriate Hilbert space {\mathbb{H}}.

Frame sets for a class of compactly supported continuous functions

2019 ◽  
Vol 13 (05) ◽  
pp. 2050093 ◽  
Author(s):  
A. Ganiou D. Atindehou ◽  
Yebeni B. Kouagou ◽  
Kasso A. Okoudjou
Keyword(s):  
Continuous Functions ◽  
Gabor Frame ◽  
Frequency Shifts ◽  
Time Frequency ◽  
Compactly Supported ◽  
Frame Set ◽  
Class Of Functions

The frame set of a function [Formula: see text] is the subset of all parameters [Formula: see text] for which the time-frequency shifts of [Formula: see text] along [Formula: see text] form a Gabor frame for [Formula: see text] In this paper, we investigate the frame set of a class of compactly supported continuous functions which includes the [Formula: see text]-splines. In particular, we add some new points to the frame sets of these functions. In the process, we generalize and unify some recent results on the frame sets for this class of functions.

scholarly journals The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates

2006 ◽  
Vol 58 (6) ◽  
pp. 1121-1143 ◽  
Author(s):  
Marcin Bownik ◽  
Darrin Speegle
Keyword(s):  
Regularity Condition ◽  
Finite Union ◽  
Gabor Frame ◽  
Gabor Frames ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Weak Regularity

AbstractThe Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.

scholarly journals Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
D. H. Yuan ◽  
Y. Feng ◽  
Y. F. Shen ◽  
S. Z. Yang
Keyword(s):  
Necessary Conditions ◽  
Gabor Frame ◽  
Frame Theory ◽  
Parseval Frame

We consider the multigenerator system{EmblTnalφl,m,n∈ℤ,l=0,…,r-1}forφ0,…,φr-1∈L2(𝕊)anda0,b0,…,ar-1,br-1>0, where the parametersb0,…,br-1>0are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame forL2(𝕊). Moreover, we present some characterizations for this system to be a Parseval frame.

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