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Pinnegar, C. R.; Wong, M. W.; Zhu, Hongmei

Integral representations of the \(TT\)-transform. (English) Zbl 1107.47032

Appl. Anal. 85, No. 8, 933-940 (2006).
The TT-transform of a signal is defined as the time-time representation of the Stockwell transform defined in the framework of Fourier multipliers or pseudo-differential operators. The authors prove two theorems each giving an integral formula for the TT-transform of signals belonging to \(L^2(\mathbb R)\).
Reviewer: Liviu Goras (Iaşi)

MSC:

47G10 Integral operators
47G30 Pseudodifferential operators
65R10 Numerical methods for integral transforms
94A12 Signal theory (characterization, reconstruction, filtering, etc.)

Keywords:

Fourier transform; Gabor transform; Stockwell transform; TT-transform; pseudodifferential operators; signals; Dawson’s integral
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References:

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