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
fDate :
12/1/1993 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
