A review on Fourier spectrum of D/A outputs with non-uniformly sampled data and time-varying clocks

Abstract

In this paper, we investigate problems of D/A converters with non-uniformly sampled input data, and/or time-varying clock sources. The input digital data (which are stored in the memory to be read out and sent to a D/A converter) were obtained by sampling an analog waveform at non-uniform sampling intervals. (Quantization of data can also be considered as a form of non-uniform sampling.) Recently, there is available a new clocking system with a very fine time resolution and is capable of adjusting the clock period in a sample-to-sample basis. With so many advances on the technology, there is a need to provide a unified theoretical model for this class of problems. In this paper, we consider the following five different models: f 1( t)=∑ n x( nT) g( t− nT), f 2( t)=∑ n x( t n ) g( t− nT), f 3( t)=∑ n x( nT) g( t− t n ), f 4( t)=∑ n x( t n ) g( t− t n ), and f 5( t)=∑ n x( t n ) g n ( t− t n ) where x(·) is the input analog signal, g(·) is the basic output pulse waveform of the D/A converter, T is the nominal sampling period and t n is the nth sampling time instance (for uniform sampling t n = nT). The first four models have been studied before [IEEE Transactions on Instrumentation & Measurements 45 (1996) 56, IEEE Transactions on Instrumentation & Measurements 46 (1997) 653] and the results are included here for completeness. The result for the fifth model is new. Closed form expressions for the Fourier transform of the output signals for each model are derived.