title: Symplectic wavelet transformation.
abstract: Usually a wavelet transform is based on dilated-translated wavelets. We propose a symplectic-transformed-translated wavelet family psi(*)(r,s)(z-kappa) (r,s are the symplectic transform parameters, |s|(2)-|r|(2)=1, kappa is a translation parameter) generated from the mother wavelet psi and the corresponding wavelet transformation W(psi)f(r,s;kappa)=integral(infinity)(-infinity)(d(2)z/pi)f(z)psi(*)(r,s)(z-kappa). This new transform possesses well-behaved properties and is related to the optical Fresnel transform in quantum mechanical version.
authors.affiliation: Department of Physics, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Hong-Yi
authors.initials: HY
authors.lastname: Fan
authors.forename: Hai-Liang
authors.initials: HL
authors.lastname: Lu