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Instantaneous Frequency and Amplitude Identification Using Wavelets: Application to Glass Structure
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| Organization: | University of Cambridge, Cambridge, U.K. |
| Organization: | University of Cambridge, Cambridge, U.K. |
| Organization: | University of Cambridge, Cambridge, U.K. |
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This paper describes a method for extracting rapidly varying, superimposed amplitude- and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet which is a modification to the well-known Morlet wavelet to allow analysis at high resolution. In order to interpret the CWT of a signal correctly, an approximate analytic expression for the CWT of an oscillatory signal is examined via a stationary-phase approximation. This analysis is specialized for the new wavelet and the results are used to construct expressions for the amplitude and frequency modulations of the components in a signal from the transform of the signal. The method is tested on a representative, variable-frequency signal as an example before being applied to a function of interest in our subject area - a structural correlation function of a disordered material - which immediately reveals previously undetected features.
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http://www.arxiv.org/abs/math-ph/0202017
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