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DSFT - Discrete Symplectic Fourier Transform

Usage

C=dsft(F);

Description

dsft(F) computes the discrete symplectic Fourier transform of F. F must be a matrix or a 3D array. If F is a 3D array, the transformation is applied along the first two dimensions.

Let F be a \(K \times L\) matrix. Then the DSFT of F is given by

\begin{equation*} C\left(m+1,n+1\right)=\frac{1}{\sqrt{KL}}\sum_{l=0}^{L-1}\sum_{k=0}^{K-1}F \left(k+1,l+1\right)e^{2\pi i\left(kn/K-lm/L\right)} \end{equation*}

for \(m=0,\ldots,L-1\) and \(n=0,\ldots,K-1\).

The dsft is its own inverse.

References:

H. G. Feichtinger, M. Hazewinkel, N. Kaiblinger, E. Matusiak, and M. Neuhauser. Metaplectic operators on cn. The Quarterly Journal of Mathematics, 59(1):15--28, 2008.