Measuring the Noise Cumulative Distribution Function Using Quantized Data

TL;DR

This paper introduces a new estimator for the cumulative distribution function and probability density function of a random variable from quantized data, applicable to real-world systems without needing detailed quantizer information.

Contribution

It proposes a novel estimator that works with quantized data without requiring knowledge of transition levels or input sequences, validated through simulations and real-world experiments.

Findings

Estimator effectively recovers distribution functions from quantized data.

The method works with uniform and non-uniform quantizers.

Experimental results demonstrate practical applicability.

Abstract

This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on the empirical distribution function that also takes the values of the quantizer transition levels into account. The properties of this estimator are discussed and analyzed at first by simulations. Then by removing all assumptions that are difficult to apply, a new procedure is described that does not require neither the transition levels nor the input sequence used to source the quantizer to be known. The experimental results obtained using a commercial 12-b data acquisition system show the applicability of this estimator to real-world type of problems.