Complex digital oscillator with absolute periodicity

In this paper, a novel control method for the coupled form complex oscillator is proposed. In this recursive structure, the roundoff errors will accumulate in time and degrade the generated sinusoids due to the finite word-length effects. The introduced control method reduces the accumulated error and forces the output sequence to be periodic. By resetting the oscillator after each discrete period, the generated sequence is made periodic and the accumulated error is canceled. Using one or two extra pair of coefficients periodically, the samples are precisely computed, and as result the accumulated error over one discrete period increases much more slowly. The presented control method allows us to design a complex digital oscillator featuring absolute periodicity, low spectral impurities, and high number of samples per cycle.