×

A basis for efficient representation of the \(S\) transform. (Chinese. English summary) Zbl 1201.94028

Summary: In order to improve the redundancy and computing capability of the \(S\) transform, a more efficient representation is presented 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 the multiple components of two time series as a function of both time and frequency. In addition, it can be defined as a generalized instantaneous frequency (IF) applicable to broadband nonstationary signals. A direct comparison between these basis functions and complex wavelets is performed, which highlights the advantages of this approach.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems

Software:

DT-CWT
PDFBibTeX XMLCite