Space-Time Fourier Transform, Convolution and Mustard Convolution

In this paper we use the steerable space-time Fourier transform (SFT), and relate the classical convolution of the algebra for spacetime Cl(3, 1)-valued signals over the space-time vector space R, with the (equally steerable) Mustard convolution. A Mustard convolution can be expressed in the spectral domain as the point wise product of the SFTs of the factor functions. In full generality do we express the classical convolution of space-time signals in terms of finite linear combinations of Mustard convolutions, and vice versa the Mustard convolution of space-time signals in terms of finite linear combinations of classical convolutions.