Quaternion Function Reference

qfft

Quaternion Fast Fourier transform

Syntax

Y = qfft(X, A, L)

Description

qfft(X, A, L) computes the Quaternion Fast Fourier Transform of the quaternion vector X using transform axis A (direction in 3-space). If X is a matrix, the transforms of the columns are computed.

L specifies the handedness of the transform ('L' or 'R') - determined by the position of the complex exponential relative to X. ('L' gives a transform with the exponential on the left of the signal.) See the related function fft which supplies a default axis and handedness.

The transform axis, A must be a pure quaternion (real or complex) but it need not have unit modulus (although the transform itself is computed using a unit-modulus axis, so that the axis is a root of -1).

This function uses the MATLAB® fft function to compute two or four complex FFTs depending on whether X is real or complex. If either or both are complex, a complex quaternion FFT is computed.

See Also

QTFM functions: iqfft, qfft2, qdft

References

  1. Ell, T. A. and Sangwine, S. J., 'Hypercomplex Fourier Transforms of Color Images', IEEE Transactions on Image Processing, 16, (1), January 2007, 22-35. DOI: 10.1109/TIP.2006.884955.
  2. Salem Said, Nicolas Le Bihan, and Stephen J. Sangwine, 'Fast complexified quaternion Fourier transform', IEEE Transactions on Signal Processing, 56, (4), April 2008, 1522-1531. DOI: 10.1109/TSP.2007.910477.

© 2008-2013 Stephen J. Sangwine and Nicolas Le Bihan

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