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iCAPs/packages/spm12/spm_dctmtx.m
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spm_dctmtx.m
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function C = spm_dctmtx(N,K,n,f)
% Create basis functions for Discrete Cosine Transform
% FORMAT C = spm_dctmtx(N)
% FORMAT C = spm_dctmtx(N,K)
% FORMAT C = spm_dctmtx(N,K,n)
% FORMAT D = spm_dctmtx(N,K,'diff')
% FORMAT D = spm_dctmtx(N,K,n,'diff')
%
% N - dimension
% K - order
% n - optional points to sample
%
% C - DCT matrix or its derivative
%__________________________________________________________________________
%
% spm_dctmtx creates a matrix for the first few basis functions of a one
% dimensional discrete cosine transform.
% With the 'diff' argument, spm_dctmtx produces the derivatives of the DCT.
%
% Reference:
% Fundamentals of Digital Image Processing (p 150-154). Anil K. Jain, 1989.
%__________________________________________________________________________
% Copyright (C) 1996-2015 Wellcome Trust Centre for Neuroimaging
% John Ashburner
% $Id: spm_dctmtx.m 6416 2015-04-21 15:34:10Z guillaume $
d = 0;
if nargin == 1, K = N; end
if nargin < 3
n = (0:(N-1))';
elseif nargin == 3
if strcmp(n,'diff')
d = 1;
n = (0:(N-1))';
elseif strcmp(n,'diff2')
d = 2;
n = (0:(N-1))';
else
n = n(:);
end
elseif nargin == 4
n = n(:);
if strcmp(f,'diff')
d = 1;
elseif strcmp(f,'diff2')
d = 2;
else
error('Incorrect Usage.');
end
else
error('Incorrect Usage.');
end
C = zeros(size(n,1),K);
if d == 0
C(:,1) = ones(size(n,1),1)/sqrt(N);
for k=2:K
C(:,k) = sqrt(2/N)*cos(pi*(2*n+1)*(k-1)/(2*N));
end
elseif d == 1
for k=2:K
C(:,k) = -2^(1/2)*(1/N)^(1/2)*sin(1/2*pi*(2*n*k-2*n+k-1)/N)*pi*(k-1)/N;
end
elseif d == 2
for k=2:K
C(:,k) = -2^(1/2)*(1/N)^(1/2)*cos(1/2*pi*(2*n+1)*(k-1)/N)*pi^2*(k-1)^2/N^2;
end
else
error('Incorrect Usage.');
end
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