Decimation for Sigma Delta Modulation

TLDR

Decimation is a key component of oversampled analog‑to‑digital conversion, converting high‑rate short words into longer words at the Nyquist rate. The study focuses on the initial decimation stage, reducing the word rate to about four times the Nyquist rate. The authors derive explicit formulas to evaluate trade‑offs among modulation rate, signal‑to‑noise ratio, word length, and the complexity of modulating and decimating functions. Digital filters composed of cascaded integrate‑and‑dump stages can match the noise structure of sigma‑delta modulation, enabling decimation with negligible loss of signal‑to‑noise ratio.

Abstract

Decimation is an important component of oversampled analog-to-digital conversion. It transforms the digitally modulated signal from short words occurring at high sampling rate to longer words at the Nyquist rate. Here we are concerned with the initial stage of decimation, where the word rate decreases to about four times the Nyquist rate. We show that digital filters comprising cascades of integrate-and-dump functions can match the structure of the noise from sigma delta modulation to provide decimation with negligible loss of signal-to-noise ratio. Explicit formulas evaluate particular tradeoffs between modulation rate, signal-to-noise ratio, length of digital words, and complexity of the modulating and decimating functions.