S Transform

S Transform

S transform as a time–frequency distribution was developed in 1994 for analyzing geophysics data. In this way, the S transform is a generalization of the short-time Fourier transform (STFT), extending the continuous wavelet transform and overcoming some of its disadvantages. For one, modulation sinusoids are fixed with respect to the time axis; this localizes the scalable Gaussian window dilations and translations in S transform. Moreover, the S transform doesn't have a cross-term problem and yields a better signal clarity than Gabor transform. However, the S transform has its own disadvantages: it requires higher complexity computation (because FFT can't be used), and the clarity is worse than Wigner distribution function and Cohen's class distribution function.

A fast S Transform algorithm was invented in 2010. It reduces the computational time and resources by at least 4 orders of magnitude and is available to the research community under an open source license.