Quantization noise in single-loop sigma-delta modulation with sinusoidal inputs
- 1 September 1989
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Communications
- Vol. 37 (9) , 956-968
- https://doi.org/10.1109/26.35376
Abstract
An exact nonlinear difference equation is derived and solved for a simple sigma-delta modulator consisting of a discrete-time integrator and a binary quantizer inside a single feedback loop and an arbitrary input signal. It is shown that the system can be represented as an affine operation (discrete-time integration of a biased input) followed by a memoryless nonlinearity. An extension of the transform method for the analysis of nonlinear systems is applied to obtain formulas for first- and second-order time-average moments of the binary quantization noise, including the sample mean, energy, and autocorrelation. The results are applied to the special case of a sinusoidal input signal to evaluate these time averages and the power spectrum. In the limit of large oversampling ratios, the marginal moments behave as if the quantization noise had a uniform distribution. The spectrum is neither white nor continuous, however, even in the limit of large oversampling ratios.<>Keywords
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