1 | function Y = qdft(X, A, L) |
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2 | % QDFT Discrete quaternion Fourier transform. |
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3 | % |
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4 | % This function computes the one-dimensional discrete quaternion Fourier |
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5 | % transform of (columns of) X, which may be a real or complex quaternion |
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6 | % array. A is the transform axis and it may be a real or complex pure |
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7 | % quaternion. It need not be a unit pure quaternion. L may take the values |
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8 | % 'L' or 'R' according to whether the hypercomplex exponential is to be |
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9 | % multiplied on the left or right of X. There are no default values. |
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10 | % |
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11 | % This function uses direct evaluation using a matrix product, and it is |
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12 | % intended mainly for verifying results against fast transform |
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13 | % implementations such as qfft.m. See also: iqdft.m. |
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14 | |
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15 | % Copyright © 2005 Stephen J. Sangwine and Nicolas Le Bihan. |
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16 | % See the file : Copyright.m for further details. |
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17 | |
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18 | error(nargchk(3, 3, nargin)), error(nargoutchk(0, 1, nargout)) |
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19 | |
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20 | if size(A) ~= [1, 1] |
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21 | error('The transform axis cannot be a matrix or vector.'); |
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22 | end |
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23 | |
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24 | if ~isa(A, 'quaternion') | ~ispure(A) |
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25 | error('The transform axis must be a pure quaternion.') |
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26 | end |
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27 | |
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28 | if L ~= 'L' & L ~= 'R' |
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29 | error('L must have the value ''L'' or ''R''.'); |
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30 | end |
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31 | |
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32 | A = unit(A); % Ensure that A is a unit (pure) quaternion. |
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33 | |
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34 | [r,c] = size(X); |
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35 | |
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36 | E = exp(-A .* 2 .* pi .* ((0:r-1)' *(0:r-1)) ./r); |
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37 | |
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38 | if L == 'L' |
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39 | Y = E * X; % Multiply the exponential matrix on the left. |
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40 | elseif L == 'R' |
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41 | Y = (X.' * E.').'; % To multiply the exponential matrix on the right |
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42 | % we transpose both and transpose the result. |
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43 | else |
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44 | error('L has incorrect value'); |
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45 | end |
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