The quaternion linear canonical transform (QLCT) is defined in this paper,\nwith proofs given for its reversibility property, its linear property, its\nodd-even invariant property and additivity property. Meanwhile, the quaternion\nconvolution (QCV), quaternion correlation (QCR) and product theorem\nof LCT are deduced. Their physical interpretation is given as classical\nconvolution, correlation and product theorem. Moreover, the fast algorithm\nof QLCT (FQLCT) is obtained, whose calculation complexity for different\nsignals is similar to FFT. In addition, the paper presents the relationship between\nthe convolution and correlation in LCT domains, and the convolution\nand correlation can be calculated via product theorem in Fourier transform\ndomain using FFT.
Loading....