The 2D Discrete Fourier Transform is given by the equation:
Which can be written as:
Since the kernel is separable, resulting in:
This important result implies that the 2D DFT F(u,v) can be obtained by
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a) | b) | c) |
The same separable form also applies for the inverse 2D DFT.
Keeping in mind that the 2D DFT can be decomposed using the 1D DFT as a primitive, we can demonstrate most of 2D Discrete Fourier Transform concepts and properties using equations related to 1D DFT.