Cm. Zierhofer, A MULTIPLIER-FREE DIGITAL SINUSOID GENERATOR BASED ON SIGMA-DELTA MODULATION, IEEE transactions on circuits and systems. 2, Analog and digital signal processing, 43(5), 1996, pp. 387-396
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.