# Dictionary:Rayleigh wavelet

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${\displaystyle f(t)=\left({\frac {1}{\pi }}\right)\left({\frac {\varepsilon }{t^{2}+\varepsilon ^{2}}}\right)}$,

where ${\displaystyle \varepsilon }$ is an arbitrary parameter that controls the width and height. This wavelet possesses a simple exact expression for its Hilbert transform [1].

## References

1. Hubral, P. and Tygel, M., 1989, Analysis of the Rayleigh pulse: Geophysics, 54, 654–658.