### ASA 124th Meeting New Orleans 1992 October

## 4aUW5. Aliasing and sampling criteria for higher-order correlations.

**Lisa A. Pflug
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*Naval Res. Lab. Detachment, Code 7173, Stennis Space Center, MS 39529
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**George E. Ioup
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Juliette W. Ioup
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*Univ. of New Orleans, New Orleans, LA 70148
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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.]