FOURIER SPECTRUM OF D/A OUTPUTS WITH NON-UNIFORMLY SAMPLED DATA AND TIME-VARYING CLOCKS

Y. C. Jenq

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. It is, therefore, interesting to consider the following question. "Given that the timing offset of each data sample is known, would it be beneficial to use this offset to adjust the read-out timing of the D/A converter?" To answer this question, we consider the following five different models: <i>f</i>₁(<i>t</i>) = &Sigma;_<i>n</i> <i>x</i>(<i>n</i> <i>T</i>) <i>g</i>(<i>t</i> - <i>n</i> <i>T</i>), <i>f</i>₂(<i>t</i>) = &Sigma;_<i>n</i> <i>x</i>(<i>t</i>_<i>n</i>) <i>g</i>(<i>t</i> - <i>n</i> <i>T</i>), <i>f</i>₃(<i>t</i>) = &Sigma;_<i>n</i> <i>x</i>(<i>n</i> <i>T</i>) <i>g</i>(<i>t</i> - <i>t</i>_<i>n</i>), <i>f</i>₄(<i>t</i>) = &Sigma;_<i>n</i> <i>x</i>(<i>t</i>_<i>n</i>) <i>g</i>(<i>t</i> - <i>t</i>_<i>n</i>), and <i>f</i>₅(<i>t</i>) = &Sigma;_<i>n</i> <i>x</i>(<i>t</i>_<i>n</i>) <i>g</i>_<i>n</i>(<i>t</i> - <i>t</i>_<i>n</i>) where <i>x</i>(.) is the input analog signal, <i>g</i>(.) is the basic output pulse waveform of the D/A converter, <i>T</i> is the nominal sampling period and <i>t</i>_<i>n</i> is the <i>n</i>-th sampling time instance (for uniform sampling <i>t</i>_<i>n</i> = <i>n</i> <i>T</i>). Closed form expressions for the Fourier transform of the output signals for each model are derived. We also discuss some potential practical applications.

Keywords

D/A converters, non-uniform sampling, Fourier spectrum

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IMEKO-TC4-2002-018.pdf

DOI

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IMEKO TC

TC4 - Measurement of Electrical Quantities

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