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 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 …

In this paper, we generalize the windowed Fourier transform to the windowed linear
canonical transform by substituting the Fourier transform kernel with the linear canonical …

One‐dimensional adaptive Fourier decomposition, abbreviated as 1‐D AFD, or AFD, is an
adaptive representation of a physically realizable signal into a linear combination of …

In a recent paper, the authors have introduced the windowed linear canonical transform and
shown its good properties together with some applications such as Poisson summation …

Recently, there has been an increasing interest in the study of hypercomplex signals and
their Fourier transforms. This paper aims to study such integral transforms from general …

Quaternion analytic signal is regarded as a generalization of analytic signal from 1D to 4D
space. It is defined by an original signal with its quaternion partial and total Hilbert …

In the framework of Clifford analysis, we consider the Paley‐Wiener type theorems for a
generalized Clifford‐Fourier transform. This Clifford‐Fourier transform is given by a similar …

Monogenic signal is regarded as a generalization of analytic signal from one dimensional to
higher dimensional space, which has been received considerable attention in the literature …

In this paper, we prove the sharp Pitt's inequality for a generalized Clifford-Fourier transform
which is given by a similar operator exponential as the classical Fourier transform but …