The S transform mathematically resembles the continuous wavelet transform but it uses Gaussian windows which do not meet a requirement of wavelet analysis, and it includes a “phase correction” that is not part of wavelet analysis. The actual use of the S-transform was simplified by performing first a forward Fourier transform of the time series. Then, for each frequency of the Fourier transform, summing the results of multiplication by a set of Fourier transforms of Gaussian windows of varying width. Finally, for each of these sums, taking the inverse Fourier transform. The equation for calculation of the S-transform of discrete time series h(kT) at time jT and frequency n/NT is where T is the sample period of the discrete time series, j is the sample index, N is the number of samples in the time series, n is the frequency index, and H[ ] is the Fourier spectrum of the discrete time series. The S-transform results in a time-frequency representation of the data. The exact code we used is a C language, S-transform subroutine available from the NIMH MEG Core
