Abstract

Usually a wavelet transform is based on dilated–translated wavelets. We propose a symplectic-transformed–translated wavelet family ψr,s*(zκ) (r,s are the symplectic transform parameters, s2r2=1, κ is a translation parameter) generated from the mother wavelet ψ and the corresponding wavelet transformation Wψf(r,s;κ)=(d2zπ)f(z)ψr,s*(zκ). This new transform possesses well-behaved properties and is related to the optical Fresnel transform in quantum mechanical version.

© 2006 Optical Society of America

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