High rate quantization analysis for a class of finite rate of innovation signals

Abstract

Acquisition and perfect reconstruction of finite rate of innovation (FRI) signals was proposed first by Vetterli, Marziliano, and Blu [1]. To the best of our knowledge, the stability of their reconstruction procedure in the presence of scalar quantizers has not been addressed in the literature. For periodic stream of Dirac FRI signal, which is an important subclass of FRI signals, the stability of reconstruction when quantization is introduced on acquired samples is analyzed in this work. It is shown that the parameters of stream of Diracs can be obtained with error O(ε), where ε is the per sample quantization error. This result holds in the high-rate quantization regime when ε is sufficiently small.