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Complex Mexican hat wavelet : ウィキペディア英語版
Complex Mexican hat wavelet

In applied mathematics, the complex Mexican hat wavelet is a low-oscillation, complex-valued, wavelet for the continuous wavelet transform. This wavelet is formulated in terms of its Fourier transform as the Hilbert analytic signal of the conventional Mexican hat wavelet:
:\hat(\omega)=\begin 2\sqrt}\pi^\omega^2 e^\omega^2} & \omega\geq0 \\()
0 & \omega\leq 0. \end
Temporally, this wavelet can be expressed in terms of the error function,
as:
:\Psi(t)=\frac}\left(\sqrt(1-t^2)e^t^2}-\left(\sqrtit+\sqrt\operatorname\left(asymptotic temporal decay in |\Psi(t)|,
dominated by the discontinuity of the second derivative of \hat(\omega)
at \omega=0.
This wavelet was proposed in 2002 by Addison ''et al.''〔(P. S. Addison, ''et al.'', ''The Journal of Sound and Vibration'', 2002 )〕 for applications requiring high temporal precision time-frequency analysis.
== References ==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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