A randomized algorithm for controlling the round-off error accumulation in recursive digital frequency synthesis (DFS)

Abstract

Recursive methods for digital frequency synthesis (DFS) exhibit numerical instability due to the round-off error propagation and accumulation in the finite precision digital computations. Because of this, despite their simplicity and other desirable features, recursive DFS methods are generally avoided in practice. In this paper we present a method that solves this numerical instability problem for the coupled form oscillator (CFO) method in a simple manner by randomizing the selection of the rotation phase-step. The internal process uncertainty, induced by the truncation of intermediate computation results, is used for randomization. Interestingly this results in the self-stabilizing property of the proposed method.