Higher-Order and Cyclostationary Statistics
Until the mid-1980’s, signal processing — signal analysis, system identification, signal estimation problems, etc. — was primarily based on second-order statistical information. Autocorrelations and cross-correlations are examples of second-order statistics (SOS). The power spectrum which is widely used and contains useful information is again based on the second-order statistics in that the power spectrum is the one-dimensional Fourier transform of the autocorrelation function. As Gaussian processes exist and a Gaussian probability density function (pdf) is completely characterised by its first two moments, the analysis of linear systems and signals has so far been quite effective in many circumstances. It has nevertheless been limited by the assumptions of Gaussianity, minimum phase systems, linear systems, etc.
KeywordsPower Spectrum Nonminimum Phase Minimum Phase System Cyclostationary Signal Power Spectral Estimate
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