Frequency Domain Min-Max Optimization of Noise-Shaping Delta-Sigma Modulators

Abstract

This paper proposes a min-max design of noise-shaping delta-sigma modulators. We first characterize the all stabilizing loop-filters for a linearized modulator model. By this characterization, we formulate the design problem of lowpass, bandpass, and multi-band modulators as minimization of the maximum magnitude of the noise transfer function (NTF) in fixed frequency band(s). We show that this optimization minimizes the worst-case reconstruction error, and hence improves the SNR (signal-to-noise ratio) of the modulator. The optimization is reduced to an optimization with a linear matrix inequality (LMI) via the generalized KYP (Kalman-Yakubovich-Popov) lemma. The obtained NTF is an FIR (finite-impulse-response) filter, which is favorable in view of implementation. We also derive a stability condition for the nonlinear model of delta-sigma modulators with general quantizers including uniform ones. This condition is described as an H-infinity norm condition, which is reduced to an LMI via the KYP lemma. Design examples show advantages of our design.

References in corpus (1)

• Signal Reconstruction via H-infinity Sampled-Data Control Theory: Beyond the Shannon Paradigm

Cited by in corpus (5)

• Rate-Distortion Analysis of Quantizers with Error Feedback
• Output Filter Aware Optimization of the Noise Shaping Properties of ΔΣ Modulators via Semi-Definite Programming
• Noise Weighting in the Design of ΔΣ Modulators (with a Psychoacoustic Coder as an Example)
• Min-Max Design of Feedback Quantizers for Netorwked Control Systems
• FIR Digital Filter Design by Sampled-Data H-infinity Discretization