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 computer code used is based closely on a C language S-transform subroutine available from the NIMH MEG Core Facility web site (http://kurage.nimh.nih.gov/meglab/). The defining equation of the S-transform is a convolution integral in continuous time. The method used is equivalent to the finite discrete time version of this, but for computational efficiency, multiplications in frequency domain are used rather than convolution in time domain. The inputs to the S-transform are real, but the outputs are complex. We use the magnitudes squared of the time-frequency output values, discarding the corresponding phase angles.
