TECHNIQUES FOR SMOOTHING AND SPLITTING IN THE CONSTRUCTION OF TIGHT FRAME GABOR WINDOWS

2013 ◽  
Vol 11 (01) ◽  
pp. 1350005
Author(s):  
SUMI JANG ◽  
BYEONGSEON JEONG ◽  
HONG OH KIM
Keyword(s):  
Sampling Rate ◽  
Tight Frame ◽  
Gabor Systems ◽  
Compactly Supported ◽  
Rational Sampling

We consider Gabor systems with compactly supported windows and rational sampling rate. Two modification techniques for tight frame Gabor windows, splitting for shorter support and smoothing for better smoothness, are introduced. As an illustration of such techniques, we construct multiwindow tight frame Gabor windows with smaller support and C∞ continuity from certain tight frame Gabor windows.

scholarly journals Wavelet frames on Vilenkin groups and their approximation properties

2015 ◽  
Vol 13 (05) ◽  
pp. 1550036 ◽  
Author(s):  
Yuri Farkov ◽  
Elena Lebedeva ◽  
Maria Skopina
Keyword(s):  
Approximation Order ◽  
Tight Frame ◽  
Explicit Description ◽  
Approximation Properties ◽  
Wavelet Frames ◽  
Vilenkin Groups ◽  
The Real ◽  
Compactly Supported

An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate Walsh polynomial is described. Approximation properties of tight wavelet frames are also studied. In contrast to the real setting, it appeared that a wavelet tight frame decomposition has an arbitrary large approximation order whenever all wavelet functions are compactly supported.

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