Relationship between quaternion linear canonical and quaternion fourier transforms

We briefly introduce the quaternion linear canonical transform (QLCT), which is a generalization of the quaternion Fourier transform (QFT) to the linear canonical transform (LCT) domain. We show that the QLCT can be reduced to the quaternion Fourier transform (QFT). We then derive the inverse transform of the QLCT using the properties of the QFT. We finally provide an example which describes the relationship between the QFT and the QLCT.