Abstract
The S-transform was originally defined as a method of determining the local spectrum of a time series, through the use of a translating, real Gaussian window that dilates to accomodate the different cycle durations of different frequencies. The S-transform “wavelet” is obtained by multiplying this real window with the complex Fourier sinusoid. Since the Fourier sinusoid has time-invariant frequency, the S-transform is consequently unsuitable for resolving waveforms whose frequency changes with time. This problem can be addressed by introducing a complex Gaussian window, with a user designed, complex phase function. The phase function modulates the frequency of the Fourier sinusoid to give a specific waveform, leading to better time–frequency localization of similar waveforms on the time series. The complex-window S-transform is similar to a wavelet transform, but has the fixed phase reference of the Fourier transform.
Published Version
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