Generalized analytic signal associated with linear canonical transform |
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Authors: | Yingxiong Fu |
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Institution: | Key Laboratory of Applied Mathematics, Hubei Province and Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China |
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Abstract: | Analytic signal is tightly associated with Hilbert transform and Fourier transform. The linear canonical transform is the generalization of many famous linear integral transforms, such as Fourier transform, fractional Fourier transform and Fresnel transform. Based on the parameter (a, b)-Hilbert transform and the linear canonical transform, in this paper, we develop some issues on generalized analytic signal. The generalized analytic signal can suppress the negative frequency components in the linear canonical transform domain. Furthermore, we prove that the kernel function of the inverse linear canonical transform satisfies the generalized analytic condition and get the generalized analytic pairs. We show the generalized Bedrosian theorem is valid in the linear canonical transform domain. |
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Keywords: | Parameter (a b)-Hilbert transform Bedrosian theorem Generalized analytic signals Linear canonical transform |
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