Development of a linear time-scale coherence spectrum

Surya Santoso; Edward J. Powers

doi:10.1117/12.255221

23 October 1996 Development of a linear time-scale coherence spectrum

Surya Santoso, Edward J. Powers

Proceedings Volume 2825, Wavelet Applications in Signal and Image Processing IV; (1996) https://doi.org/10.1117/12.255221
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

In spectral analysis of two or more signals, it is desirable to quantify the statistical relationships among them. The linear coherence spectra based on Fourier analysis have been widely used to quantify the linear relationships between two stationary fluctuating signals. However, in the case of nonstationary signals, the Fourier-based linear coherence spectrum has a limited utility, since temporal information is now required. It is the purpose of this paper to extend the notion of the classical linear coherence spectra to the time-scale coherence spectrum. it will be shown that not only is the new time-scale coherence spectrum capable of measuring linear relationships between two nonstationary signals in the time-scale domain but also of detecting their phase differences as well. Using the Cauchy-Schwarz inequality, it can be shown that the time-scale coherence spectrum is bounded by zero and one. The latter number indicates a perfect linear relation between the two nonstationary signals at a particular time and scale. The efficacy of the new method is demonstrated and compared with that of the classical coherence spectrum through numerical examples.

Citation Download Citation

Surya Santoso and Edward J. Powers "Development of a linear time-scale coherence spectrum", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); https://doi.org/10.1117/12.255221

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KEYWORDS

Signal detection

Wavelet transforms

Interference (communication)

Statistical analysis

Phase shifts

Signal to noise ratio

Signal analyzers

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