DocumentCode
1015977
Title
The Zak transform and sampling theorems for wavelet subspaces
Author
Janssen, Augustus J E M
Author_Institution
Appl. Math. Group, Philips Res. Lab., Eindhoven, Netherlands
Volume
41
Issue
12
fYear
1993
fDate
12/1/1993 12:00:00 AM
Firstpage
3360
Lastpage
3364
Abstract
The Zak transform is used for generalizing a sampling theorem of G. Waiter (see IEEE Trans. Informat. Theory, vol. 38, p. 881-884, 1992) for wavelet subspaces. Cardinal series based on signal samples f(a+n), n∈Z with a possibly unequal to 0 (Waiter´s case) are considered. The condition number of the sampling operator and worst-case aliasing errors are expressed in terms of Zak transforms of scaling function and wavelet. This shows that the stability of the resulting interpolation formula depends critically on a
Keywords
interpolation; series (mathematics); signal processing; stability; wavelet transforms; Zak transform; cardinal series; interpolation formula; sampling operator; sampling theorem; sampling theorems; scaling function; signal samples; stability; wavelet subspaces; worst-case aliasing errors; Convergence; Discrete Fourier transforms; Fourier transforms; Interpolation; Mathematics; Sampling methods; Stability; Wavelet analysis; Wavelet transforms;
fLanguage
English
Journal_Title
Signal Processing, IEEE Transactions on
Publisher
ieee
ISSN
1053-587X
Type
jour
DOI
10.1109/78.258079
Filename
258079
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