A MULTIPLIER-FREE DIGITAL SINUSOID GENERATOR BASED ON SIGMA-DELTA MODULATION

In this paper sigma-delta (Sigma-Delta) sequences derived from a singl e-loop numeric Sigma-Delta modulator with sinusoidal input are investi gated. A class of limit cycles shows a special kind of symmetry, desig nated as ''half-symmetry''. It is shown that half-symmetric Sigma-Delt a sequences are especially suited for automatic generation by means of an autonomous oscillator, The design of such an oscillator is present ed. The central part Is a single-loop numeric Sigma-Delta modulator. T he two-level output sequence of the Sigma-Delta modulator is accumulat ed in lossless discrete integrators and fed back to the input, If the initial conditions of the oscillator registers are chosen properly in relation to a system constant F, the oscillator generates a two-level Sigma-Delta sequence identical to the sequence of a Sigma-Delta modula tor which is externally driven by a pure sinusoid. Conditions for syst em constant F and initialization for periodic operation are derived, I f constant F is an integer, the operation of the oscillator is exclusi vely based on integers. Thus, although the network is highly recursive , truncation- or roundoff errors are avoided and problems with respect to stability do not occur.