There have been numerous proposals in the literature to generalize the classical Fourier
transform by making use of the Hamiltonian quaternion algebra. The present paper reviews …

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 …

In this review, we give an overview of several recent generalizations of the Fourier transform,
related to either the Lie algebra or the Lie superalgebra. In the former case, one obtains …

We survey the development of Clifford's geometric algebra and some of its engineering
applications during the last 15 years. Several recently developed applications and their …

We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we
establish an uncertainty principle for the right-sided QFT. This uncertainty principle …

We generalize the linear canonical transform (LCT) to quaternion‐valued signals, known as
the quaternionic linear canonical transform (QLCT). Using the properties of the LCT we …

Complex analysis is one of the most interesting areas in mathematics. Methods of complex
function theory have proven to be useful for the treatment of plane problems of mathematical …

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 …

Linear canonical transforms (LCTs) are a family of integral transforms with wide application
in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier …

Convolution and correlation operations are very important in signal processing community,
as well as in sampling, filter design and applications. In this study, the authors derive the …