How the 2D FFT works

This is part of an online course on foundations and applications of the Fourier transform. The course includes 4+ hours of video lectures, pdf readers, exercises, and solutions.

Each of the video lectures comes with MATLAB code, Python code, and sample datasets for applications. With 3000+ lines of code, this course is also a great way to improve your programming skills.

[fdmeneses]

Thank you Mike!! After going through so many videos, I can now finally understand how the two axis interplay. Well done!

[BaillehachePascal]

I spent hours looking at other videos or web pages to try to understand why my implementation of the 2D FFT didn't work, and finally that's your video which clarified everything ! Thank you so much !!!

[johnlovesmath]

Dr. Mike, your linear algebra book is so good. The sections on SVD and intro PCA are explained so well. This video just answered my question too, thanks for all you do.

[godsart]

Great explanation - exactly what I was looking for to fill in some gaps in my knowledge. You did some of the experiments I was curious about. Thanks.

[fr]

Bro you’re the goat! Great explanation 🫡

[scottpbwowepic]

This is amazing, great explanation, was able to give some intuition about something unintuitive (to me)

[INCYTER]

Thanks for this - Much appreciated. Well done, and well explained!

[saimadhavp]

Mike, Your videos generally hits the bulls eye. Focusing on extremely critical parts and its nuances of overall concepts, which generally is missed by others. I am looking for little more info on how to elicit out Frequencies and amplitudes from the resultant matrix output. Whether it is DFT ot FFT. Can you provide further pointers.

[mszawerd]

But why when calculating 2D transform we are first calculating transform for columns, and then transform for rows of the previous result? Why this works? Why we are not calculating transform for columns, and for rows of the input image and then adding it together like in calculating 2D derivative?

[tsehayenegash]

Thank you to upload this video. I have a question. how can I evaluate Phase and Amplitude at a given temperature data?

[berkeberkeme]

Could you please tell how to obtain the frequency of a cartesian point on fouriered image in matlab

[JiffyJokes]

I applied the 1D fft in matlab by using fft(X, [ ], 1) for an FFT of the 7x7 matrix to get the values like at 1:24 but I get different results

[QuyetNguyen-sgdq]

how to do match between input image and template image? if I use FFT

[aayush]

I have a 512 x 81 matrix in matlab. The matrix represents a image. There is clutter in the image. How do I generate image from that matrix and remove the clutter??

[subhashiskar]

I want he code for python. If not then MATLAB is ok. Actually I want to build something like this in my final year project.

[gaiuspliniussecundus]

So, when you transform to frequency space, you loose the ability to, e.g., edit a single pixel in the spatial domain. Because you decorrelated the pixels into freq and phase components?

[georgeevans]

How can I get the matlab code used in the video? What tool box is required ?

[muhammadfikriarifardi]

I am sorry, its just me or to hear you I need a bigger speaker

[prasadradhika]

Nice video. Could you please tell how to obtain the frequency in 2D Fourier transform spectrum in Python?

[itWouldBeWise]

When you say at 2:07 that for images the DC frequencies are shifted to the center, is that just for displaying the frequency spectrum? Or is it necessary for using it e.g. to apply a gaussian filter convolution via the convolution theorem?