The Two-Dimensional Discrete Fourier Transform

The two-dimensional discrete Fourier transform (DFT) is the natural extension of the one-dimensional DFT and describes two-dimensional signals like images as a weighted sum of two dimensional sinusoids. Two-dimensional sinusoids have a horizontal frequency component and a vertical frequency component and play an important role in image processing and compression.

[@jimraptis1899]

The best Discrete Fourier explanation found on YT so far. Well done!!!

[@vaaal88]

Absolutely best explanation on this topic I have found anywhere. Thank you!

[@Itzak15]

My teacher just showed the 2D transformation formula and told us to remember it for the exam 💀

[@NoerLuin]

Finally this clicked for me. Thank you so much.

[@Archturian8880]

Thank you. This is the best explanation ever.

[@omitbadgers5664]

Thanks a lot!

[@chemoukid2270]

Very well explained! thank you very much indeed

[@benwinstanleymusic]

Thank you very clear

[@glenyeldho5782]

Can you make videos about wavelet transform !!

[@mansoorwahab8934]

yes please

[@sunanthony191]

At the slide 5, why x[m,n] is in the X[k,l] (DFT coeffs) ? As X[k,l] are the weights of x[m,n], but we need x[m,n] to find X[k,l]. that sounds weired.

[@aravindaanil9482]

best explanation

[@xiluo8714]

This video really helps! Thanks~~

[@shaulchamoula4863]

Thank you so much for that excellent explanation.
Can I ask for a reference to a code implementation of that transform?

[@LiuZicheng-cw5nk]

The subtitles' default language setting needs to be corrected. It's English, obviously. Why set Russian?

[@sutharsanmahendren179]

Sir Thank you so much for your explanation. What is the reference book you are using

[@AG-cx1ug]

At 7:59 to calculate x[k,l] what would we input for k and l in e^(-j2pi(k/N) * m)?

[@allsignalprocessing]

k and l are the specific indices associated with the signal. Typically they would vary from 0 to N-1 if you reconstruct the entire signal. You can reconstruct it at any subset of values too.

[@jacobvandijk6525]

Thanks. Is 2D DFT what is used in MRI?

[@AG-cx1ug]

what is N here?

[@allsignalprocessing]

It is the number of values in each coordinate direction. If an image, it assumes an N by N image of pixels.