A multiplier-free digital sinusoid generator based on sigma-deltamodulation

摘要

In this paper sigma-delta (Σ-Δ) sequences derived fromna single-loop numeric Σ-Δ modulator with sinusoidal inputnare investigated, A class of limit cycles shows a special kind ofnsymmetry, designated as “half-symmetry”. It is shown thatnhalf-symmetric Σ-Δ sequences are especially suited fornautomatic generation by means of an autonomous oscillator. The design ofnsuch an oscillator is presented. The central part is a single-loopnnumeric Σ-Δ modulator. The two-level output sequence of thenΣ-Δ modulator is accumulated in lossless discretenintegrators and fed back to the input. If the initial conditions of thenoscillator registers are chosen properly in relation to a systemnconstant F, the oscillator generates a two-level Σ-Δnsequence identical to the sequence of a Σ-Δ modulator whichnis externally driven by a pure sinusoid. Conditions for system constantnF and initialization for periodic operation are derived, If constant Fnis an integer, the operation of the oscillator is exclusively based onnintegers. Thus, although the network is highly recursive, truncation- ornroundoff errors are avoided and problems with respect to stability donnot occur