Cauchy wavelet
In mathematics, Cauchy wavelets are a family of continuous wavelets, used in the continuous wavelet transform. == Definition == The Cauchy wavelet of order p {\displaystyle p} is defined as: ψ p ( t ) = Γ ( p + 1 ) 2 π ( j t + j ) p + 1 {\displaystyle \psi _{p}(t)={\frac {\Gamma (p+1)}{2\pi }}\left({\frac {j}{t+j}}\right)^{p+1}} where p > 0 {\displaystyle p>0} and j = − 1 {\displaystyle j={\sqrt {-1}}} therefore, its Fourier transform is defined as ψ p ^ ( ξ ) = ξ p e − ξ I [ ξ ≥ 0 ] {\displaystyle {\hat {\psi _{p}}}(\xi )=\xi ^{p}e^{-\xi }I_{[\xi \geq 0]}} .