Multi-channel sampling expansion for band-pass signals without channels constraints

Abstract

The aim of the multi-channel sampling expansion (MSE) is the reconstruction of an unknown continuously defined function ft, from the samples of the responses of m linear time invariant (LTI) systems, each sampled by the 1/m th Nyquist rate. The MSE for band-pass signals in the Fourier transform (FT) domain has recently been presented in the literature under some restricted conditions. To be specific, a necessary condition for perfect reconstruction of a band-pass signals is discussed which requires the number of filters/channels m in the system must be even. Focusing on this issue, first, based on a quadrature representation of the band-pass signal, we propose a new MSE. It is shown that perfect signal reconstruction is possible for any arbitrary number of channels when the upper cutoff frequency is a multiple of the bandwidth. Then, in order to show the importance of the MSE scheme, we apply the recurrent non-uniform sampling scheme to analyze high-rate waveform digitizers. The parallel architecture utilizes the interleaving/multiplexing techniques to extend the capabilities of the monolithic analog/digital (A/D) converter technology. Last, the MSE of band-pass signal is improved which can allow multiple sampling rates in the system.