On mathematical derivations of auto-term functions and signal-to-noise ratios of the Choi--Williams, first- and nth-order hyperbolic kernels

Authors:
Khoa N. Le;Kishor P. Dabke;Gregory K. Egan
Affiliations:
Department of Electrical and Computer Systems Engineering, Clayton, Monash University, Victoria, Australia;Department of Electrical and Computer Systems Engineering, Clayton, Monash University, Victoria, Australia;Department of Electrical and Computer Systems Engineering, Clayton, Monash University, Victoria, Australia
Venue:
Digital Signal Processing
Year:
2006

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Abstract

This paper continues investigations on the hyperbolic kernel family [K.N. Le et al., Opt. Eng. 42 (8) (2003) 2400-2415] by giving further mathematical insight into auto-term and noise robustness properties of the first-order hyperbolic, Choi-Williams (CW) and nth-order hyperbolic kernels, for which explicit expressions are derived and approximated for useful values of kernel control parameters @b, @s and kernel order n. Simulation results are also given to support the mathematical approximations.