A Sampling Algorithm of Non-band Limited Signals Based on SVD

Abstract

We combined the finite rate of innovation (FRI) method with singular value decomposition (SVD) theory and got an improved sampling algorithm of non-band limited signals. It used SVD instead of annihilating filter in FRI method to reduce noise. We took streams of diracs signal as an example and deduced the detailed sampling and reconstruction process in the improved algorithm. It first found DFT coefficients of the samples, and constructed a Hankel data matrix. Then the matrix was decomposed according to SVD technique and the position information of diracs was gotten. Finally it computed weight coefficients from the Vandermonde system. The simulation results indicate that the original signal can also be reconstructed well in the presence of noise if only the sample rate is not less than its innovation rate. The sampling method based on SVD has good antinoise performance. It also saves power consumption and computational complexity. In some communication systems such as UWB and CDMA, a very narrow pulse which is like diracs signal very much is used to carry information. So this FRI algorithm based on SVD can be applied in their receivers.