On the aliasing error in wavelet subspaces

Shannonʹs sampling formula has been extended to subspaces { V j } j ∈ Z in multiresolution analysis. When we apply the corresponding sampling formula for V 0 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 V 1 . We obtain an expression for its Fourier transform, Ef ^ , which allows us to give estimations of the aliasing error both in L 2 ( R ) -norm and in L ∞ ( R ) -norm. Finally, we carry out a study of the aliasing error in the case when f belongs to V 2 .