Time-varying frequencies of a signal

Patrick J. Loughlin

doi:10.1117/12.284182

24 October 1997 Time-varying frequencies of a signal

Patrick J. Loughlin

Proceedings Volume 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII; (1997) https://doi.org/10.1117/12.284182
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

We consider the definition and interpretation of instantaneous frequency and other time-varying frequencies of a signal, and related concepts of instantaneous amplitude, instantaneous bandwidth and the time-varying spectrum of a signal. A definition for the average frequency at each time is given, and we show that spectrograms and Cohen-Posch time-frequency distributions can yield this result for the first conditional moment in frequency. For some signals this result equals the instantaneous frequency, but generally instantaneous frequency is not the average frequency at each time in the signal. We discuss monocomponent versus multicomponent signals, and give an estimate of the time-varying spectrum given the instantaneous frequencies and bandwidths of the components. We also consider the role of the complex signal in defining instantaneous amplitude, frequency and bandwidth, and ways to obtain a complex signal satisfying certain physical properties, given a real signal (or its time-varying spectrum). Depending upon the physical properties desired (e.g., the instantaneous amplitude of a magnitude-bounded signal should itself be bounded), one obtains different complex representations -- and hence different instantaneous amplitudes, frequencies and bandwidths -- of the given signal.

Citation Download Citation

Patrick J. Loughlin "Time-varying frequencies of a signal", Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997); https://doi.org/10.1117/12.284182

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