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Multistage sigma-delta modulation

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3 Author(s)
Chou, W. ; Dept. of Electr. Eng., Stanford Univ., CA, USA ; Wong, P.W. ; Gray, R.M.

A theoretical basis is provided for multistage sigma-delta modulation (MSM), which is a cascade realization of several single-loop sigma-delta modulators with a linear combinatorial network. Equations are derived describing the output and the quantization noise of MSM for an arbitrary input signal, and the noise-shaping characteristic of MSM is investigated. The spectral characteristics of an m-stage sigma-delta modulator with both DC and sinusoidal inputs are developed. For both types of inputs the binary quantizer noise of the mth (m⩾3) quantizer, which appears at the output as an m th order difference, is asymptotically white, uniformly distributed, and uncorrelated with the input level. It is also found that for an m-stage sigma-delta quantizer with either an ideal low-pass filter or a sincm+1 filter decoder, the average quantization noise of the system is inversely proportional to the (2m+1)th power of the oversampling ratio. This implies that the high-order systems are favourable in terms of the trade-off between the quantization noise and oversampling ratio. Simulation results are presented to support the theoretical analysis

Published in:

Information Theory, IEEE Transactions on  (Volume:35 ,  Issue: 4 )