Interconnections Between Multiplier Methods and Window Methods in Generalized Sampling

摘要

The use of multipliers in the time domain or windows in the frequency domain are two favorite ways of producing kernels in generalized sampling. In this paper we study interconnections. First we consider bandlimited kernels. One of the main results implies that every interpolating window method is a multiplier method. We also give a complete description of the shape of those windows. Finally, we extend these results to non-bandlimited kernels obtained by using either a non-bandlimited multiplier or a window that is not compactly supported. In both cases the Gaussian function is an example that has been much considered in the literature.