# Fourier 4 - The Fourier transform in 2D and 3D

**URL:** <https://forum.microlist.org/t/fourier-4-the-fourier-transform-in-2d-and-3d/2841>\
**Category:** Announcements\
**Created:** [October 8, 2024, 10:51am UTC](https://forum.microlist.org/t/fourier-4-the-fourier-transform-in-2d-and-3d/2841 "2024-10-08T10:51:26Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![P\_Tadrous](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.microlist.org/p_tadrous/32/862_2.png) [@P\_Tadrous](https://forum.microlist.org/u/P_Tadrous)\
**Post date:** [October 8, 2024, 10:51am UTC](https://forum.microlist.org/t/fourier-4-the-fourier-transform-in-2d-and-3d/2841/1 "2024-10-08T10:51:26Z")

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My latest teaching video on the Fourier transform discusses the extension of the DFT into multiple dimensions with applications to image processing. Any of you who want to learn Abbe’s diffraction theory of imaging in the light microscope or who use deconvolution microscopy should find this relevant background info:

[![](https://us1.discourse-cdn.com/flex020/uploads/microlist/original/2X/8/895d8f70a17c46d65e08ba0fea2b9ac23bdd35e0.jpeg "Fourier 4 - The DFT in 2D and 3D") ](https://www.youtube.com/watch?v=E8qWBaal6LM)

# CONTENTS

00:00 Context  
00:40 Sinusoids in 2D and 3D  
04:21 The resultant (1D) wave  
06:48 The principle of separability - how to do a 2D/3D DFT  
11:36 Polar vs. rectangular coordinates (arg, mod, power)  
16:05 The importance of phase (argument)  
20:17 Image scaling in the Fourier domain  
22:00 Image filtering in the Fourier domain  
24:33 Summary