A method of time-time analysis: The TT-transform

A novel technique of analysis of an arbitrary primary time series into a set of secondary, timelimited, local, constituent time series, the TT-transform, is presented. The time–time representation is derived from the S-transform, a method of representation of a real time series as a set of complex, time-localized spectra. When integrated over time, the S-transform becomes the Fourier transform of the primary time series. Similarly, when summed over the primary time variable, the TT-transform reverts to the primary time series. The invertibility of the TT-transform points to the possibility of filtering and signal to noise improvements in the time domain, and some insight into the localized spectra of the S-transform.  2003 Elsevier Inc. All rights reserved.