Digital-to-analog (D/A) converters with nonuniformly sampled signals

In this paper, we investigate the problem of the D/A converter with nonuniformly sampled input data. The input digital data were obtained by sampling the intended analog waveform at nonuniform time intervals, and we look into the question: "Given that the timing offset of each data sample is known, would it be beneficial, in terms of the output signal-to-noise ratio, to use this offset to adjust the playback timing of the D/A converter?" We examine two different timing strategies. The first approach simply plays out the signal at a uniform rate, while the second one uses the known timing offset to adjust the D/A converter playback timing accordingly. The closed-form expressions of the spectrum of the D/A converter output signals are derived. From these expressions, we find that the spectrum structure, for the case where the timing offsets are compensated, is the infinite sum of the weighted shift to the baseband spectrum. For the uniform playout approach, the spectrum structure is much more complicated where each shifted spectrum is modified by a different weighting function of the frequency. Although the spectrum structure may be conceptually simpler for the case where the timing offsets are compensated, it is by no means clear that either method is better than the other in terms of the output waveform quality. We then apply the results to analyze the direct digital synthesis output sine waves. The signal-to-noise ratio, SNR, for both cases is derived in simple closed form. It is found that for the case where the timing offsets are compensated, the SNR can be greatly enhanced by appropriate selection of operation parameters.