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:
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