The Zak transform and sampling theorems for wavelet subspaces
- 1 January 1993
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 41 (12), 3360-3364
- https://doi.org/10.1109/78.258079
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 aKeywords
This publication has 3 references indexed in Scilit:
- Two theorems on lattice expansionsIEEE Transactions on Information Theory, 1993
- A sampling theorem for wavelet subspacesIEEE Transactions on Information Theory, 1992
- Ten Lectures on WaveletsPublished by Society for Industrial & Applied Mathematics (SIAM) ,1992