# 12. Define discrete Fourier transform and its inverse.

## 12. Define discrete Fourier transform and its inverse.

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