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a/gabor/zak.m b/gabor/zak.m
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function c=zak(f,a);
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function c=zak(f,a);
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%ZAK  Zak transform
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%ZAK  Zak transform
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%   Usage:  c=zak(f,a);
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%   Usage:  c=zak(f,a);
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%
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%
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%   ZAK(f,a) computes the Zak transform of f with parameter _a.
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%   zak(f,a) computes the Zak transform of *f* with parameter *a*.  The
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%   The coefficients are arranged in an _a x _L/a matrix, where _L is the
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%   coefficients are arranged in an $a \times L/a$ matrix, where *L* is the
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%   length of f.
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%   length of *f*.
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%
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%
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%   If f is a matrix, then the transformation is applied to each column.
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%   If *f* is a matrix then the transformation is applied to each column.
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%   This is then indexed by the third dimension of the output.
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%   This is then indexed by the third dimension of the output.
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%
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%
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%   Assume that $c=zak(f,a)$, where *f* is a column vector of length *L* and
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%   $N=L/a$. Then the following holds for $m=0,\ldots,a-1$ and $n=0,\ldots,N-1$
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%
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%
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%   Assume that c=ZAK(f,a), where f is a column vector of length L and
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%   ..                     N-1
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%   N=L/a. Then the following holds for $m=0,...,a-1$ and $n=0,...,N-1$
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%     c(m+1,n+1)=1/sqrt(N)*sum f(m-k*a+1)*exp(2*pi*i*n*k/N)
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%                          k=0
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%
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%
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%M                         N-1
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%M    c(m+1,n+1)=1/sqrt(N)*sum f(m-k*a+1)*exp(2*pi*i*n*k/N)
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%M                         k=0
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%F  \begin{eqnarray*}
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%F  c(m+1,n+1) & = & \frac{1}{\sqrt{N}}\sum_{k=0}^{N-1}f(m-ka+1)e^{2\pi ink/M}
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%   .. math:: c(m+1,n+1) = \frac{1}{\sqrt{N}}\sum_{k=0}^{N-1}f(m-ka+1)e^{2\pi ink/M}
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%F  \end{eqnarray*}
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%
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%
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%
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%
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%   References: ja94-4 bohl97-1
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%   References: ja94-4 bohl97-1
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...
...
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% of the Zak transform.
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% of the Zak transform.
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c(:,:,ii)=dft(reshape(f(:,ii),a,N),[],2);
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c(:,:,ii)=dft(reshape(f(:,ii),a,N),[],2);
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end;
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end;
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%OLDFORMAT