Sampling Approximations for Time- and Bandlimiting

摘要

This paper extends work of Shen and Walter and others concerning relationships between sampling and time-frequency localization. We consider approximate projections onto eigenspaces of time- and bandlimiting operators, expressed in terms of samples of bandlimited functions. We establish error estimates of eigenfunction samples and on matrices that can be used to generate approximations of these samples. Numerical comparisons are made between approximations generated by a method proposed by Walter, Shen and Soleski and an alternative method proposed by Karoui and Moumni.