Hyperbolic kernel for time-frequency power spectrum

We propose a new family of hyperbolic kernels Φhyperbolic(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.