Quadratic time-frequency distributions: The new hyperbolic class and its intersection with the affine class
Date of Original Version
The proposed new class of quadratic time-frequency distributions is based on the 'hyperbolic time shift' and scale invariance properties that are important in the analysis of Doppler invariant signals used in bat and dolphin echolocation, and of 'locally self-similar' signals used in fractals and fractional Brownian motion. The hyperbolic class can be characterized by 2-D kernels, and kernel constraints are derived for some desirable TFD properties. The Bertrand distribution and the Altes distribution are members of the hyperbolic class. The authors define a 'localized' subclass and study the intersection between the affine class and the hyperbolic class.
1992 IEEE 6th SP Workshop on Statistical Signal and Array Processing, SSAP 1992 - Conference Proceedings
Papandreou, A., F. Hlawatsch, and G. F. Boudreaux-Bartels. "Quadratic time-frequency distributions: The new hyperbolic class and its intersection with the affine class." 1992 IEEE 6th SP Workshop on Statistical Signal and Array Processing, SSAP 1992 - Conference Proceedings , (1992): 26-29. doi:10.1109/SSAP.1992.246840.