Affiliation:
1. School of Mathematical Science Yangzhou University Yangzhou 225002 China
2. School of Mathematics and Statistics Beijing Institute of Technology Beijing 100081 China
Abstract
The quaternion linear canonical transform (QLCT) has been widely used in color image processing. Biquaternion is a more generalized algebra of quaternion, which has attracted scholars' research interest in recent years. In this paper, a new transform is proposed called the biquaternion linear canonical transforms (BiQLCTs). Due to the noncommutativity of biquaternion algebra multiplication, there are three different types of the BiQLCTs: Left‐sided BiQLCT, right‐sided BiQLCT, and two‐side BiQLCT. The transforms are the extension of the complex linear canonical transforms. Then, the relationships between the three kinds of transforms are obtained. Next, based on the right‐side biquaternion linear canonical transform (RBiQLCT), some general properties of this transform are proved. Moreover, the convolution and correlation theorems of the RBiQLCT are studied. As an application, according to the convolution operator and convolution theorem, the biquaternion linear time‐invariant system is analyzed. Finally, the Heisenberg uncertainty principle for the RBiQLCT is established.
Funder
National Key Research and Development Program of China
National Natural Science Foundation of China
Subject
General Engineering,General Mathematics
Reference30 articles.
1. Least squares Hermitian problem of a kind of quaternion tensor equation
2. A novel calibration method of SINS/DVL integration navigation system based on quaternion;Xu B.;IEEE Sens. J.,2020
3. Further research on exponential stability for quaternion-valued neural networks with mixed delays
4. Uncertainty principles associated with quaternionic linear canonical transforms
5. A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform;Bahri M.;Symmetry‐Basel,2022