  Fourier transform (FT) plays a crucial role in a broad range of applications,
from enhancement, restoration and analysis through to security, compression and
manipulation. The Fourier transform (FT) is a process that converts a function
into a form that describes the frequencies. This process has been extended to
many domains and numerical representations (including quaternions). However, in
this article, we present a new approach using dual-quaternions. As
dual-quaternions offer an efficient and compact symbolic form with unique
mathematical properties. While dual-quaternions have established themselves in
many fields of science and computing as an efficient mathematical model for
providing an unambiguous, un-cumbersome, computationally effective means of
representing multi-component data, not much research has been done to combine
them with Fourier processes. Dual-quaternions are simply the unification of
dual-number theory with hypercomplex numbers; a mathematical concept that
allows multi-variable data sets to be transformed, combined, manipulated and
interpolated in a unified non-linear manner. We define a Dual-Quaternion
Fourier transform (DQFT) for dual-quaternion valued data over dual-quaternion
domains. This opens the door to new types of analysis, manipulation and
filtering techniques. We also present the Inverse Dual-Quaternion Fourier
Transform (IDQFT). The DQFT unlocks the potential provided by hypercomplex
algebra in higher dimensions useful for solving dual-quaternion partial
differential equations or functional equations (e.g., for multicomponent data
analysis)
