Partial differential equations (PDEs) see widespread use in sciences and engineering to
describe simulation of physical processes as scalar and vector fields interacting and …

We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and
investigate QFT properties useful for applications. Different forms of the QFT lead us to …

The new applications of Clifford's geometric algebra surveyed in this paper include
kinematics and robotics, computer graphics and animation, neural networks and pattern …

Sound is a fundamental and rich source of information; playing a key role in many areas
from humanities and social sciences through to engineering and mathematics. Sound is …

Quaternions are extensively used in several fields including physics, applied mathematics,
computer graphics, and control systems because of their notable and unique characteristics …

Quaternion and Clifford Fourier Transforms describes the development of quaternion and
Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first …

To solve the estimation problem in three-dimensional space, the quaternion Kalman filter
(QKF) is developed for quaternion-valued signals using the well-known minimum mean …

Digital watermarking technology, as a powerful tool for copyright protection and content
authentication of multimedia works, has received increasing attention, and the current image …

While the existing quaternion principal component analysis (QPCA) is a linear tool
developed mainly for processing linear quaternion signals, the quaternion representation …

In view of the fact that it is difficult to predict the location and size of the failure of rotating
machinery, the sensors sometimes cannot collect the fault information. When the fault …