# Dictionary:Rayleigh wavelet

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