The right-sided quaternion linear canonical transform is obtained by substituting the Fourier kernel
with the right-sided QFT kernel in the LCT definition, and so on.
Chunyu, "A performance comparison of SVMs based on Fourier kernel
and RBF kernel," Journal of Chongqing University of Posts and Telecommunications (Natural Science), vol.
where x = [x.sub.1] [e.sub.1] + [x.sub.2][e.sub.2], [omega] = [[omega].sub.1][e.sub.1] + [[omega].sub.2][e.sub.2] and the quaternion exponential product [mathematical expression not reproducible] is the quaternion Fourier kernel
. Here [F.sub.q] is called the quaternion Fourier transform operator.
The fact that the coefficient [C.sub.n] is a sample of f arises from the fact that the Fourier kernel
[e.sup.-i[omega]t]/[square root of 2[pi]] has the property that when one of its arguments takes successively the values n, (n [member of] Z), an orthonormal basis for [L.sup.2](-[pi], [pi]) results.
Fox, The G and H functions as symmetrical Fourier Kernels