A First-Order Markov Model for Understanding Delta Modulation Noise Spectra

A first-order Markov process is used to model the sequence of quantization noise samples in delta modulation. An autocorrelation parameter in the Markov model controls the shape of the noise spectrum, and as decreases from 1 to 0 and then to -1, the spectrum changes from a low-pass to a flat, and then to a high-pass characteristic. One can also use the Markov model to predict the so-called out-of-band noise rejection that is obtained when delta modulation is performed with an oversampled input, and the resulting quantization noise is lowpass filtered to the input band. The noise rejection is a function of as well as an oversampling factor and an interesting asymptotic result is that if . Delta modulation literature has noted the importance of the special values, and . These correspond to autocorrelation values of 0 and -1/3.