On the aliasing error in wavelet subspaces

摘要

Shannon's sampling formula has been extended to subspaces {Vj}j∈Z in multiresolution analysis. When we apply the corresponding sampling formula for V0 to a function which does not belong to this space, the so-called aliasing error arises. This paper deals with the aliasing error, Ef, whenever f is in V1. We obtain an expression for its Fourier transform, Ef^, which allows us to give estimations of the aliasing error both in L2(R)-norm and in L∞(R)-norm. Finally, we carry out a study of the aliasing error in the case when f belongs to V2.