Pinnegar, C. R.; Mansinha, L. Time-local Fourier analysis with a scalable, phase-modulated analyzing function: The \(S\)-transform with a complex window. (English) Zbl 1151.94329 Signal Process. 84, No. 7, 1167-1176 (2004). Summary: 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. Cited in 4 Documents MSC: 94A11 Application of orthogonal and other special functions 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 94A14 Modulation and demodulation in information and communication theory Keywords:time-frequency analysis; waveform analysis; short-time Fourier transform; wavelet transform; \(S\)-transform PDFBibTeX XMLCite \textit{C. R. Pinnegar} and \textit{L. Mansinha}, Signal Process. 84, No. 7, 1167--1176 (2004; Zbl 1151.94329) Full Text: DOI