- Title
- The Hilbert space geometry of the Rihaczek distribution for stochastic analytic signals
- Creator
- Scharf, Louis L.; Schreier, Peter J.; Hanssen, Alfred
- Relation
- IEEE Signal Processing Letters Vol. 12, Issue 4, p. 297-300
- Publisher Link
- http://dx.doi.org/10.1109/LSP.2005.843772
- Publisher
- IEEE Signal Processing Society
- Resource Type
- journal article
- Date
- 2005
- Description
- The Rihaczek distribution for stochastic signals is a time- and frequency-shift covariant bilinear time-frequency distribution (TFD) based on the Cramér-Loevè 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.
- Subject
- commentary correlation; Cramér-Loevè spectral representation; nonstationary time series; frequency analysis; improper complex random process
- Identifier
- uon:1611
- Identifier
- http://hdl.handle.net/1959.13/27373
- Identifier
- ISSN:1070-9908
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