Digital spectra of non-uniformly sampled signals with applications to digitally synthesized sinusoids

The overwhelming majority of the digital signal processing theories developed so far have been concentrated on uniformly sampled signals. In this paper we develop a systematic approach to compute the digital spectra of a class of digital signals obtained by nonuniformly sampling analog signals. This development is motivated by the need to characterize the spectral property of a digitally synthesized sinusoidal waveform. The full representation of the spectral components of a digitally synthesized sinusoidal signal is derived. From that representation, we prove some important properties which provide great insight into the spectral characteristics of a digitally synthesized sinusoid.