Uncertainty Principle for a Kind of Quaternionic Linear Canonical Transform
一类四元数线性正则变换的不确定性原理

应雄 付
2014 Advances in Applied Mathematics  
Hartley transform is a generalization of Fourier transform and it transforms the real signal into real signal thereby reducing the amount of computation. In recent years, with the wide applications of fractional Fourier transform in signal processing, linear canonical transform has gradually been applied to signal processing. Hence, it is a valuable problem to generalize Hartley transform in linear canonical transform domain. In this paper, a kernel function with conjugate property is obtained
more » ... operty is obtained by changing kernel function of Hartley transform in Fourier transform domain. After that, we obtain Hartley transform in linear canonical transform domain by using kernel function of linear canonical transform. Then, Hartley transform in linear canonical transform domain has the properties of real number and odd-even invariance. Finally, by using Heisenberg uncertainty principle in linear canonical transform domain, we obtain Heisenberg uncertainty principle of Hartley transform in linear canonical transform domain. Citation: Li Y G, Zhang C. Hartley transform for linear canonical transformation and uncertainty principle[J]. Opto-Electronic Engineering, 2018, 45(6): 170743
doi:10.12677/aam.2014.33020 fatcat:6ckdrll6xfbsfogpcqkyvrjhri