Generalized sampling theorem for bandpass signals

The reconstruction of an unknown continuously defined function f( t) from the samples of the responses of m linear time-invariant (LTI) systems sampled by the 1/mth Nyquist rate is the aim of the generalized sampling. Papoulis ( 1977) provided an elegant solution for the case where f ( t) is a band-limited function with finite energy and the sampling rate is equal to 2/m times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST) for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed. Copyright (C) 2006 Hindawi Publishing Corporation. All rights reserved.