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

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1 Author(s)
Jayant, N.S. ; Bell Labs., Murray Hill, NJ, USA

A first-order Markov process is used to model the sequence of quantization noise samples in delta modulation. An autocorrelation parameter C in the Markov model controls the shape of the noise spectrum, and as C 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 G is a function of C as well as an oversampling factor F and an interesting asymptotic result is that G=frac{1-C}{1+C} \dot F if F \gg frac{1+C}{1-C} \dot frac{\pi}{2} . Delta modulation literature has noted the importance of the special G values, F and 2F . These correspond to autocorrelation values of 0 and -1/3.

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Communications, IEEE Transactions on  (Volume:26 ,  Issue: 8 )