Adaptive Gabor frames by projection onto time-frequency subspaces

2014 ◽  
Author(s):  
Monika Dorfler ◽  
Gino Angelo Velasco
Keyword(s):  
Gabor Frames ◽  
Time Frequency

Constructing super Gabor frames: the rational time-frequency lattice case

2010 ◽  
Vol 53 (12) ◽  
pp. 3179-3186 ◽  
Author(s):  
ZhongYan Li ◽  
DeGuang Han
Keyword(s):  
Gabor Frames ◽  
Time Frequency

DIRECTIONAL TIME–FREQUENCY ANALYSIS VIA CONTINUOUS FRAMES

2015 ◽  
Vol 92 (2) ◽  
pp. 268-281 ◽  
Author(s):  
OLE CHRISTENSEN ◽  
BRIGITTE FORSTER ◽  
PETER MASSOPUST
Keyword(s):  
Frequency Analysis ◽  
Gabor Frames ◽  
Wavelet Frames ◽  
Gabor Systems ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
B Splines ◽  
Meyer Wavelet ◽  
Continuous Frames ◽  
General Frames

Grafakos and Sansing [‘Gabor frames and directional time–frequency analysis’, Appl. Comput. Harmon. Anal.25 (2008), 47–67] have shown how to obtain directionally sensitive time–frequency decompositions in $L^{2}(\mathbb{R}^{n})$ based on Gabor systems in $L^{2}(\mathbb{R})$. The key tool is the ‘ridge idea’, which lifts a function of one variable to a function of several variables. We generalise their result in two steps: first by showing that similar results hold starting with general frames for $L^{2}(\mathbb{R}),$ in the settings of both discrete frames and continuous frames, and second by extending the representations to Sobolev spaces. The first step allows us to apply the theory to several other classes of frames, for example wavelet frames and shift-invariant systems, and the second one significantly extends the class of examples and applications. We consider applications to the Meyer wavelet and complex B-splines. In the special case of wavelet systems we show how to discretise the representations using ${\it\epsilon}$-nets.

scholarly journals Gabor Frames and Time-Frequency Analysis of Distributions

1997 ◽  
Vol 146 (2) ◽  
pp. 464-495 ◽  
Author(s):  
Hans G. Feichtinger ◽  
K Gröchenig
Keyword(s):  
Frequency Analysis ◽  
Gabor Frames ◽  
Time Frequency Analysis ◽  
Time Frequency

scholarly journals Varying the time-frequency lattice of Gabor frames

2003 ◽  
Vol 356 (5) ◽  
pp. 2001-2023 ◽  
Author(s):  
Hans G. Feichtinger ◽  
Norbert Kaiblinger
Keyword(s):  
Gabor Frames ◽  
Time Frequency
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