Title :
Model Space Results for the Gabor and Wavelet Transforms
Author :
Ascensi, Gerard ; Bruna, Joaquim
Author_Institution :
Fac. of Math., Univ. of Vienna, Vienna
fDate :
5/1/2009 12:00:00 AM
Abstract :
We prove that the unique Gabor window leading to an analytic model space is the Gaussian one, and we give an analogous result for the wavelet transform. For the general case we give a new approach to study irregular Gabor and wavelet frames. We improve some known results for Gabor windows in the Feichtinger algebra, and for a special class of wavelets.
Keywords :
algebra; wavelet transforms; Feichtinger algebra; space model; unique Gabor window; wavelet transforms; Algebra; Continuous wavelet transforms; Harmonic analysis; Mathematics; Particle measurements; Sampling methods; Signal analysis; Time frequency analysis; Wavelet analysis; Wavelet transforms; Continuous transform; Gabor system; frames; sampling sets; wavelets;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2009.2016028
