Average Aliasing Error for General Prefiltering Based on Shift Invariant Spaces

The conventional A/D conversion has been extended to the A/D conversions based on shift invariant spaces, in which, the pre-filtering is performed by quasi-projections into shift invariant spaces and sampling is performed in the shift invariant spaces. This paper studies the accuracy of the extended prefiltering. As a contribution of this paper, a formula to exactly evaluate the average aliasing error is established. Furthermore, for a signal in Sobolev space, removing the restriction that the exponent of Sobolev space is greater than 1/2 imposed by the previous authors, this paper finds that the average aliasing error decays at the rate as the exponent of the Sobolev space.