12. Define discrete Fourier transform and its inverse.
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The discrete Fourier transform pair that applies to sampled function is given by,
For u = 0, 1, 2 . . . . , N-1, and
For x = 0, 1, 2 . . . ., N-1.
In the two variable case the discrete Fourier transform pair is
For u = 0, 1, 2 . . . , M-1, v = 0, 1, 2 . . . , N - 1, and
For x = 0, 1, 2 . . . , M-1, y = 0, 1, 2 . . . , N-1.
If M = N, then discrete Fourier transform pair is
For u, v = 0, 1, 2 . . . , N – 1, and
For x, y = 0, 1, 2 . . . , N – 1
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