Generalizing the TT-transform

The TT-transform is a method of dividing a primary time series into a set of secondary, time-localized time series, through use of a translatable, scalable Gaussian window. These secondary time series resemble ordinary windowed time series, except that higher frequencies are more strongly concentrated around the midpoint of the Gaussian, as compared with lower frequencies. In this paper the TT-transform is generalized to accommodate arbitrary scalable windows. The generalized TT-transform can be useful in resolving the times of event initiations when used jointly with a related time–frequency distribution, the generalized S-transform.