A comparison of several optimal random quantization algorithms for correlation estimation

The estimation of the correlation function is a problem which is becoming increasingly important in the area of signal processing. It requires a very large quantity of date. In order to minimize computations it is advisable to encode the data, with a minimal number of useful quantization levels. Consequently, we are interested in computing the autocorrelation function, for several kinds of random quantizers [i.e quantizer with random transition points] with low quantization levels. In the first part, we shall deal with the importance of the random quantization principle which makes it possible to cancel the estimation bias [is the case of an infinite quantizer]. This is not the case with the deterministic quantizer [D.Q.]. We shall examine three types of random quantizers : the non-uniform random quantizer [N.U.R.Q.], the uniform random quantizer [U.R.Q.] and the random quantizer with exponential steps [R.Q.E.]. This last is interesting in the sense that it allows a coding requiring no multiplications. In the second part we shall examine the performances of these optimum quantizers when they are applied to parameter estimation of an Auto Regressive model. Two measures of distance are studied : the spectral distance and the cepstral distance, with special attention being paid to the latter.