Sigma-delta modulation with i.i.d. Gaussian inputs

The response of a single-loop sigma-delta modulator to an independent identically distributed (i.i.d.) Gaussian input signal is analyzed. A continuous-time stochastic model is developed and the connection of the model to the system is described. A condition is given so that the difference between the behavior of the model and that of the true system can be made arbitrarily small. Theories from renewal and Wiener processes are applied to show the convergence and mixing properties of the output sequence. Also derived is the power spectrum of the quantization noise. Compared to the spectrum when the input is DC, the i.i.d. Gaussian random process smears the discrete spectrum into band structures.<
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