Multi-loop sigma-delta quantization: spectral analysis

Abstract

An exact spectral analysis of oversampled discrete-time L-loop (L>or=2) sigma-delta modulator ( Sigma Delta M) with DC (constant) input is presented. It is shown by a novel application of ergodic theory that the embedded quantizer error sequence is asymptotically uniformly distributed, white and uncorrelated with the input, a fact usually assumed a priori in the linearized models. It was found that for the following linear demodulators: (1) optimum FIR (finite-impulse response) filter, (2) sinc/sup k/ filters (k>or=L+1), and (3) the ideal low-pass filter, the overall system ( Sigma Delta M plus demodulator) can provide a normalized average quantization noise power inversely proportional to the (2L+1)-st power of the oversampling ratio, confirming the performance superiority of multiloop Sigma Delta M over single-loop Sigma Delta M.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>