Eckahrd Hitzer, General Two-Sided Quaternion Fourier Transform, Convolution and Mustard Convolution, Advances in Applied Clifford Algebras, Online First: 12th May 2016, DOI: 10.1007/s00006-016-0684-8, Preprint: http://vixra.org/abs/1601.0165
Abstract: In this paper we use the general two-sided quaternion Fourier transform (QFT), and relate the classical convolution of quaternion-valued signals over $\R^2$ with the Mustard convolution. A Mustard convolution can be expressed in the spectral domain as the point wise product of the QFTs of the factor functions. In full generality do we express the classical convolution of quaternion signals in terms of finite linear combinations of Mustard convolutions, and vice versa the Mustard convolution of quaternion signals in terms of finite linear combinations of classical convolutions.
Keywords: Convolution, Mustard convolution, two-sided quaternion Fourier transform, quaternion signals, spatial domain, frequency domain