The Zak Transform and Sampling Theorems for
Wavelet Subspaces · 1993
The Zak transform is used for generalizing a sam- pling theorem of G. Walter for wavelet subspaces. Cardinal series based on signal samples f(a + n), n E 2 with a possibly unequal to 0 (Walter's case) are considered. The condition number of the sampling operator and worst-case aliasing er- rors are expressed in terms of Zak transforms of scaling func- tion and wavelet. This shows that the stability of the resulting interpolation formula depends critically on a.