  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.
