Selecting the optimal sampling rate for the waveform generator with a variable clock

Abstract

The broad sampling rate range of the Waveform Generator with Variable Clock (WGVC) allows unlimited choices. Selecting the sample rate only based on the Nyquist criterion might cause aliasing, when the mirror frequency is below the cut frequency of WGVC's reconstruction filter. Replaying signals using the maximum sample rate of the WGVC requires arbitrary sample rate conversion (ASRC), which has a high computational cost. Previous work proposed a suboptimal method to retrieve a fraction for converting the initial waveform in a WGVC with fractional sample rate conversion (FSRC), which guarantees anti-aliasing and a low computation cost. In this paper, an algorithm based on continued fractions is proposed to select a conversion fraction within a closed interval for FSRC, which not only ensures that the numerator and denominator are minimized theoretically but also avoids inversion errors caused by floating-point calculations. Experimental results demonstrate that the computational cost of signal conversion and waveform storage requirements are reduced when this algorithm is applied. In addition, the spectral purity of the output signal is better than that of the ASRC algorithm using the proposed algorithm.