Measuring the Noise Cumulative Distribution Function Using Quantized Data

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 nonuniform 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. Experimental results obtained using a commercial 12-bit data acquisition system show the applicability of this estimator to real-world type of problems.

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