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

Khoa N. Le; Kishor P. Dabke; Gregory K. Egan

doi:10.1016/j.dsp.2005.04.006

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

Khoa N. Le, Kishor P. Dabke, Gregory K. Egan

Western Sydney University

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

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 Î², Ïƒ and kernel order n. Simulation results are also given to support the mathematical approximations.

Original language	English
Pages (from-to)	84-104
Number of pages	21
Journal	Digital Signal Processing
Volume	16
Issue number	1
DOIs	https://doi.org/10.1016/j.dsp.2005.04.006
Publication status	Published - 2006

Keywords

approximation theory
kernel functions
signal processing

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10.1016/j.dsp.2005.04.006

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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 {\^I}², {\"I}ƒ and kernel order n. Simulation results are also given to support the mathematical approximations.",

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AU - Egan, Gregory K.

PY - 2006

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N2 - 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 Î², Ïƒ and kernel order n. Simulation results are also given to support the mathematical approximations.

AB - 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 Î², Ïƒ and kernel order n. Simulation results are also given to support the mathematical approximations.

KW - approximation theory

KW - kernel functions

KW - signal processing

UR - http://handle.uws.edu.au:8081/1959.7/uws:37684

U2 - 10.1016/j.dsp.2005.04.006

DO - 10.1016/j.dsp.2005.04.006

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EP - 104

JO - Digital Signal Processing

JF - Digital Signal Processing

IS - 1

ER -

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

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