A new subclass of complex-valued S-transform windows

The S-transform is a time–frequency representation whose analyzing function is the product of a fixed Fourier sinusoid with a scalable, translatable window. Thus the S-transform combines elements of wavelet transforms and windowed Fourier transforms. The S-transform can also be generalized to include windows that have frequency-dependent functional form, and frequency-dependent complex phase modulation, essentially giving phase-shifted wavelets which have no semblance at different scales. However, their frequency-dependent shapes can become so complicated that the resulting time–frequency S-spectra are impossible to interpret. In this paper, I define a subclass of complex-valued S-transform windows whose amplitude and phase modulations are connected to each other, making the resulting S-spectra easier to interpret.