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Discrete linear canonical transforms based on dilated Hermite functions

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Abstract

Linear canonical transform (LCT) is very useful and powerful in signal processing and optics. In this paper, discrete LCT (DLCT) is proposed to approximate LCT by utilizing the discrete dilated Hermite functions. The Wigner distribution function is also used to investigate DLCT performances in the time–frequency domain. Compared with the existing digital computation of LCT, our proposed DLCT possess additivity and reversibility properties with no oversampling involved. In addition, the length of input/output signals will not be changed before and after the DLCT transformations, which is consistent with the time–frequency area-preserving nature of LCT; meanwhile, the proposed DLCT has very good approximation of continuous LCT.

© 2011 Optical Society of America

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