Integral representations of the TT-transform

Abstract

The TT-transform of a signal is defined to be the time–time representation of the Stockwell transform that gives the time–frequency information of the signal. Two integral representations of the TT -transform are given.

Keywords:

• Fourier transform
• Gabor transform
• Stockwell transform
• TT-transform
• Pseudo-differential operators
• Signals
• Dawson's integral

Keywords:

• Mathematics Subject Classifications (2000): Primary: 47G10
• 47G30
• 65R10
• Secondary: 92C55
• 94A12

Acknowledgement

This research has been supported by the Natural Sciences and Engineering Research Council of Canada.