QuaternionFourierTransform.jl

Discrete Quaternion Fourier Transform for Julia.

Requirements

• Quaternions.jl (not official package)

Installation

pkg> add https://github.com/peakbook/Quaternions.jl
pkg> add https://github.com/peakbook/QuaternionFourierTransform.jl

Example

using Quaternions
using QuaternionFourierTransform

qmat = imag(rand(QuaternionF64, 10, 10))

# QFT
qfreq = qft(qmat)

# IQFT
iqmat = iqft(qfreq)

# Convolution
qfilter = ...
qconv(qmat, qfilter)

You can specify the orthonormal basis as follows:

# Default value is `QuaternionFourierTransform.defaultbasis`
q = (quaternion(0,1,0,0),quaternion(0,0,1,0),quaternion(0,0,0,1))
qft(m, mu=q)

See example.

Reference

• Ell, T. A. and Sangwine, S. J., ``Hypercomplex Fourier Transforms of Color Images,'' IEEE Transactions on Image Processing, 16, (1), January 2007.
• Quaternion and octonion toolbox for Matlab, http://qtfm.sourceforge.net/