2D DFT from 1D DFT

[Laboratory]

The 2D Discrete Fourier Transform is given by the equation:

displaymath166

Which can be written as:

displaymath167

Since the kernel is separable, resulting in:

displaymath168

This important result implies that the 2D DFT F(u,v) can be obtained by

  1. taking the 1D DFT of every row of image f(x,y), F(u,y),
  2. take the 1D DFT of every column of F(u,y)

a)f(x,y); b)F(u,y); c)F(u,v)
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.





Main DIP Menu
DIP Feedback Form
Copyright © 1997-1995 KRI, ISTEC, Ramiro Jordán, Roberto Lotufo. All Rights Reserved