The Bispectrum of Sampled Data: Part I—detection of the Sampling Jitter

The effect of timing error (jitter) on the power spectrum (second-order spectrum) of sampled data has been investigated previously. The current increasing interest in higher-order spectra calls for investigation of the effect of sampling jitter on the discrete higher-than-order-two spectra. In this paper, we present results concerning the bispectrum (third-order spectrum). We derive expressions for the bispectrum of sampled data under the assumption that the timing errors are independently identically distributed (i.i.d.) random variables. It is shown that, while the discrete bispectrum of a uniformly sampled third-order stationary signal is zero in a triangle that is a proper subset of the principal domain, it differs from zero in the presence of jitter. Exploiting this effect, we propose a test for detection of sampling jitter, using the bispectrum. Namely, given estimates of the discrete bispectrum of an unknown band-limited signal, we can decide whether jitter is present or not. The performance of the proposed detector is analyzed, and its dependence on the jitter variance, signal skewness, and observation time is shown.