Aliasing and sampling criteria for higher-order correlations

Abstract

While sampling data at a Nyquist frequency equal to the highest frequency present in the data (critical sampling) is sufficient to prevent aliasing in both the data and the discrete-time autocorrelation calculated from the data of a bandlimited energy signal, the sampling requirements for the avoidance of aliasing in higher-order correlations are not necessarily the same. They depend on whether one samples the continuous-time autobicorrelation or autotricorrelation directly, for which critical sampling is sufficient, or whether these quantities are calculated from sampled data, in which case it is not. For the latter, the sampling interval for the autobicorrelation must be no greater than two-thirds the interval associated with critical sampling, and no greater than one-half for the autotricorrelation. Numerical calculations of autobicorrelation and autotricorrelation zero-lag values corresponding to spectral area and volume, as well as bispectral contour plots, for example, bandlimited deterministic signals, are presented as illustrations. Spectral and convolutional masking filters which remove aliasing in higher-order correlations calculated from critically sampled data are presented. Differences in frequency content for rectified signals and in aliasing for autocorrelations sampled directly or calculated from sampled data are also discussed. [Work supported by ONR/NRL-SSC.]