The Hilbert space geometry of the Rihaczek distribution for stochastic analytic signals

The Rihaczek distribution for stochastic signals is a time- and frequency-shift covariant bilinear time-frequency distribution (TFD) based on the Crame acute;r-Loe grave;ve spectral representation for a harmonizable process. It is a complex Hilbert space inner product (or cross correlation) between the time series and its infinitesimal stochastic Fourier generator. To this inner product, we may attach an illuminating geometry, wherein the cosine squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek distribution. The Rihaczek distribution also determines a time-varying Wiener filter for estimating a time series from its infinitesimal stochastic Fourier generator and measures the resulting error covariance. We propose a factored kernel to construct estimators of the Rihaczek distribution that are contained in Cohen’s class of bilinear TFDs.