Hyperbolic kernel for time-frequency power spectrum

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

doi:10.1117/1.1590651

1 August 2003 Hyperbolic kernel for time-frequency power spectrum

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

Optical Engineering, Vol. 42, Issue 8, (August 2003). https://doi.org/10.1117/1.1590651

We propose a new family of hyperbolic kernels Φ_hyperbolic(θ,τ) = [sech(βθτ)]ⁿ, where n = 1,3,5,... for a joint time-frequency distribution. The first-order hyperbolic kernel sech(βθτ) is mainly considered. Theoretical aspects of the new hyperbolic kernel are examined in detail. The effectiveness of a kernel is determined by three factors: cross-term suppression, auto-term resolution, and noise robustness. The effectiveness of the new kernel is compared with other kernels including Choi-Williams, Wigner-Ville, and multiform tiltable exponential using two different signals: complex-exponential and chirp.

©(2003) Society of Photo-Optical Instrumentation Engineers (SPIE)

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Khoa Nguyen Le, Kishor P. Dabke, and Gregory K. Egan "Hyperbolic kernel for time-frequency power spectrum," Optical Engineering 42(8), (1 August 2003). https://doi.org/10.1117/1.1590651

Published: 1 August 2003

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