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A 2D DFT Example

Consider a real 2D signal:

\begin{displaymath}{\bf x}_r=\left[
\begin{array}{rrrrrrrr}
0.0 & 0.0 & 0.0 & 0...
...& 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0
\end{array} \right]
\end{displaymath}

The imaginary part ${\bf x}_i={\bf0}$. The 2D Fourier spectrum ${\bf X}$ of this signal can be found by 2D DFT. The real part of the spectrum is:

\begin{displaymath}{\bf X}_r = \left[
\begin{array}{r\vert rrr\vert r\vert rrr} ...
...-32.7 & 1.6 & -21.0 & 13.2 & 27.7 & -11.3
\end{array} \right] \end{displaymath}

and the imaginary part of the spectrum is:

\begin{displaymath}{\bf X}_i = \left[
\begin{array}{r\vert rrr\vert r\vert rrr} ...
...0 & -16.8 & 30.2 & -6.9 & 27.1 & -89.2 \\
\end{array} \right] \end{displaymath}

Pay close attention to the even and odd symmetry of the spectrum.



Ruye Wang 2003-11-17