Quaternion Function Reference

mustard

Mustard convolution

Syntax

R = mustard(f, g, mu, H)

Description

R = mustard(f, g, mu, H) returns the so-called 'Mustard' convolution of f and g. This is the convolution equivalent to pointwise multiplication of the Fourier transforms of f and g. It is dependent on the definition of the Fourier transform. This function assumes a one-sided QFT as computed by qfft and qfft2 using a transform 'axis' mu and a handedness H as defined in the parameter profiles of the transforms. The computation performed by the mustard function does not use Fourier transforms: it is computed using convolutions, but these convolutions differ according to the equivalent transform axis and handedness.

This code handles one dimensional or two dimensional arrays f and g according to the parameters supplied. If they are vectors, they must be both row or both column vectors.

References

  1. David Mustard, 'Fractional convolution', The Journal of the Australian Mathematical Society, Series B, Applied Mathematics, Vol 40, 257­265, 1998. DOI: 10.1017/S0334270000012509.
  2. De Bie, H.; De Schepper, N.; Ell, T. A.; Rubrecht, K. and Sangwine, S. J., 'Connecting spatial and frequency domains for the quaternion Fourier transform', Applied Mathematics and Computation, 271, 581-593, 15 November 2015, DOI: 10.1016/j.amc.2015.09.045.

(c) 2008-2016 Stephen J. Sangwine and Nicolas Le Bihan

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