The Zak transform and sampling theorems for wavelet subspaces

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 in 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.<>