Hermitian wavelet
Hermitian wavelets are a family of discrete and continuous wavelets used in the constant and discrete Hermite wavelet transforms. The n th {\displaystyle n^{\textrm {th}}} Hermitian wavelet is defined as the normalized n th {\displaystyle n^{\textrm {th}}} derivative of a Gaussian distribution for each positive n {\displaystyle n} : Ψ n ( x ) = ( 2 n ) − n 2 c n He n ( x ) e − 1 2 x 2 , {\displaystyle \Psi _{n}(x)=(2n)^{-{\frac {n}{2}}}c_{n}\operatorname {He} _{n}\left(x\right)e^{-{\frac {1}{2}}x^{2}},} where He n ( x ) {\displaystyle \operatorname {He} _{n}(x)} denotes the n th {\displaystyle n^{\textrm {th}}} probabilist's Hermite polynomial.