Novel designs of recursive discrete-time sinusoidal oscillators

This paper presents novel designs of multi-output sinusoidal oscillators derived from recursive digital filter structures. Two methods to design a complex digital oscillator were developed. In the first approach we obtain the output signals as a result of using in the oscillator algorithm the desired rotation matrix elements, while in the second approach the recipe is opposite: based on the desired amplitudes and phases of sinusoidal signals we obtain the rotation matrix elements. The common feature of these two strategies is the rotation matrix ability to unify various complex oscillator structures. Detailed analysis of the complex oscillators yielded to design multi-output sinusoidal oscillators with waveforms of specified amplitudes and phases. The three-phase oscillator proposed here can be implemented with the aid of four multipliers having two different coefficient values, three adders, and three delay elements.