Kalman filtering and time-frequency distribution of random signals

P. G. Madhavan; William J. Williams

doi:10.1117/12.255430

22 October 1996 Kalman filtering and time-frequency distribution of random signals

P. G. Madhavan, William J. Williams

Proceedings Volume 2846, Advanced Signal Processing Algorithms, Architectures, and Implementations VI; (1996) https://doi.org/10.1117/12.255430
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

A new method to estimate the energy distribution over the time-frequency plane of time-varying stochastic signals is presented. A state space modeling approach is used to represent the signal. A Kalman-smoothing algorithm is used to estimate the states from which the so-called `Kalman- smoothed time frequency distribution (KS-TFD)' is obtained. The KS-TFD estimate is positive, has good cross-term properties and high temporal resolution. The Kalman smoother-based estimates are optimal in the mean square sense and therefore the KS-TFD estimate has excellent noise performance. We demonstrate the `localizing' property of KS- TFD using deterministic signals such as impulses and Gabor logons. Minimum interference is seen with multi component signals. For Gabor logons buried in white noise at various signal-to-noise ratios, we show the excellent performance of the KS-TFD estimate in comparison to the non-causal spectrogram using quantitative performance indices.

Citation Download Citation

P. G. Madhavan and William J. Williams "Kalman filtering and time-frequency distribution of random signals", Proc. SPIE 2846, Advanced Signal Processing Algorithms, Architectures, and Implementations VI, (22 October 1996); https://doi.org/10.1117/12.255430

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KEYWORDS

Signal to noise ratio

Time-frequency analysis

Filtering (signal processing)

Interference (communication)

Electronic filtering

Smoothing

Stochastic processes

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