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Fourier transforms in image processing

Posted on December 1, 2021December 1, 2021 By christo No Comments on Fourier transforms in image processing

The Fourier transform produces another representation of a signal, specifically a representation as a weighted sum of complex exponentials. Because of Euler’s formula

ejq =cos(q) + jsin(q)

where j2 = −1, we can say that the Fourier transform produces a representation of a (2D) signal as a weighted sum of sines and cosines. The defining formulas for the forward Fourier and the inverse Fourier transforms are as follows. Given an image a and its Fourier transform A, then the forward transform goes from the spatial domain (either continuous or discrete) to the frequency domain which is always continuous

The specific formulas for transforming back and forth between the spatial domain and the frequency domain are given below

Table of Contents

  • In 2D continuous space:
  • In 2D discrete space:

In 2D continuous space:

Fourier transforms
In 2D continuous space:

In 2D discrete space:

In 2D continuous space
In 2D continuous space

image processing Tags:Fourier transforms, image processing

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