An exact spectral analysis of a number controlled oscillator based synthesizer

An exact analysis of a number controlled oscillator (NCO)-based synthesizer is presented. A description of an NCO-based synthesizer is provided. A continuous Fourier transform is developed for an arbitrary stepped waveform like a direct digital synthesizer (DDS) output. A method for generating the mapping PROM used by a DDS is described, so that the output waveform distortion is minimized. Computer-based calculations are presented to provide insight to the workings of a DDS. Among other results it is shown that the output cleanliness is not a function of the number of phase bits in the NCO. Rather, the phase bits in the NCO simply represent the resolution with which frequencies may be selected.<>