On the TT-Transform and Its Diagonal Elements

The TT-transform stands for time-time transform and has been derived as an inverse Fourier transform of the time-frequency
S
-transform. Up to date, only the diagonal of the TT-transform has been used for signal characterization. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this transform. In particular, we demonstrate that the diagonal elements of the TT-transform represent a simple frequency filtered version of the original signal and, thus, that little additional information is gained through the TT-transform.