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Write an expression for a 2D-DFT. What is its relationship with one dimension DFT? How one-dimensional FFT algorithm can be used to compute two dimensional DFT of a digital image.
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teamques10
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By 2D Fourier Transform,
$F(u,v) = \frac{1}{N} \sum_{x=0}^{N-1} \sum_{y=0}^{N-1} f(x,y) W_N^{xu} W_N^{yv}$
Row Transform∶
$F(u,v) = \frac{1}{N} \sum_{x=0}^{N-1} W_N^{xu} \sum_{y=0}^{N-1} f(x,y)W_N^{yv} \\ F(u,v) = \frac{1}{N} \sum_{x=0}^{N-1} W_N^{xu} F(x,v)$
Column Transform∶
$F(u,v)=\frac{1}{N} \sum_{x=0}^{N-1}F(x,v) W_N^{xu}$
2D Fourier Transform of input image can be obtained by performing row-wise 1D transform followed by column-wise …
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