Resampling and requantization of band-limited Gaussian stochastic signals with flat power spectrum

TL;DR

This paper provides a theoretical framework and efficient algorithms for analyzing the degradation effects of resampling and requantization on band-limited Gaussian signals with flat power spectrum, validated by numerical experiments.

Contribution

It introduces a novel analytical approach using Fourier transforms to characterize the joint probability distribution of quantized signals after resampling and requantization.

Findings

The analytical expressions closely match numerical results.

The approach efficiently computes degradation metrics.

Numerical experiments confirm the theoretical predictions.

Abstract

A theoretical analysis, aimed at characterizing the degradation induced by the resampling and requantization processes applied to band-limited Gaussian signals with flat power spectrum, available through their digitized samples, is presented. The analysis provides an efficient algorithm for computing the complete {joint} bivariate discrete probability distribution associated to the true quantized version of the Gaussian signal and to the quantity estimated after resampling and requantization of the input digitized sequence. The use of Fourier transform techniques allows deriving {approximate} analytical expressions for the quantities of interest, as well as implementing their efficient computation. Numerical experiments are found to be in good agreement with the theoretical results, and confirm the validity of the whole approach.