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5.1 Discrete Fourier Transform
dft(X)
- Replaces the columns of a dense complex matrix with their discrete
Fourier transforms: if X has n rows,
![\begin{displaymath}
X[k,:] := \sum_{j=0}^{n-1} e^{-2\pi j k \sqrt{-1}/n} X[j,:],
\qquad k=0,\ldots,n-1.
\end{displaymath}](img72.gif)
idft(X)
- Replaces the columns of a dense complex matrix with their inverse
discrete Fourier transforms: if X has n rows,
![\begin{displaymath}
X[k,:] :=
\frac{1}{n} \sum_{j=0}^{n-1} e^{2\pi j k \sqrt{-1}/n} X[j,:],
\qquad k=0,\ldots,n-1.
\end{displaymath}](img73.gif)
The separable discrete two dimensional Fourier transform first computes the corresponding one dimensional transform along the columns of the matrix, followed by the one dimensional transform along the rows of the matrix.
dft2(X)
-
Replaces a dense complex matrix with the two dimensional discrete Fourier transform.
idft2(X)
-
Replaces a dense complex matrix with the inverse two dimensional discrete Fourier transform.