A Basis for Efficient Representation of the S Transform

In order to improve the redundancy and computing capability of S transform,a more efficient representation is introduced,by introducing an orthogonal set of basis functions that localizes the spectrum and retains the advantageous phase properties of the S-transform.These basis functions are defined to have phase characteristics that are directly related to the phase of the Fourier transform spectrum,and are both compact in frequency and localized in time.Therefore it can perform localized cross spectral analysis to measure phase shifts between each of multiple components of two time series as a function of both time and frequency.In addition,if can be defined that a generalized instantaneous frequency(IF) applicable to broadband nonstationary signals.A direct comparison between these basis functions and complex wavelets is performed,highlighting the advantages of this approach.