Multiple frequencies and AR parameters estimation from one bit quantized signal via the EM algorithm

A novel algorithm to estimate the coefficient of q AR (autoregressive) processes from a coarsely quantized signal is presented. The input signal to the quantizer is the superposition of qAR processes and noise. In a related problem a modified version of the above algorithm is used to estimate the frequencies of closely quantized data obtained from q sinusoids embedded in noise. The proposed algorithm can accommodate a nonuniform m-level quantizer, as well as the special case of 1-b quantizer. The proposed estimator is based on the maximum likelihood (ML) criterion and is realized here by judiciously combining the expectation-maximization algorithm of A.D. Dempster et al. (1977) and the Gaussian fit scheme. Simulations reveal that one can accurately estimate the coefficients of several AR processes, or the frequencies of several sinusoids by using 1-b quantized data at low signal to noise ratios and moderate number of observations