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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 parameterCin the Markov model controls the shape of the noise spectrum, and asCdecreases 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 rejectionGis a function ofCas well as an oversampling factorFand an interesting asymptotic result is thatG=frac{1-C}{1+C} dot FifF gg frac{1+C}{1-C} dot frac{pi}{2}. Delta modulation literature has noted the importance of the specialGvalues,Fand2F. These correspond to autocorrelation values of 0 and -1/3.

Published in:

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

Date of Publication:

Aug 1978

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