In a previous post, the variance of the in-band quantization noise for a first order sigma delta modulator was derived. Taking it one step furhter, let us find the variance of the quantization noise filtered by a second order filter.
With a first order filter, the quantization noise passes through a system with transfer function [...]
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In an earlier post, it was mentioned that delta modulator without the quantizer is identical to convolving an input sequence with . Let us first try to validate that thought using a small MATLAB example and using the delta modulator circuit shown in Figure 9.13a of DSP-Proakis [1].
% delta modulation
xn = sin(2*pi*1/64*[0:63]);
xhatn = 0;
for [...]
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