Computing Derivatives with FFT [Matlab]

[@howardhuang8433]

Probably an unforeseen outcome of current events is that students in the future will have so much online material to learn from. Thank you for putting this out there!

[@brschlegs]

It’s amazing to me that not only do you post these in depth videos, but you link both your code and the PDF of your book to each video.. Thank you for what you do, I wish I had these resources when I was in undergrad!!

[@martynsnwaokocha6982]

My professor recommended this and I must say it's a very good illustration. Thanks

[@michaelsun7968]

Watched the whole series on the Fourier Analysis, amazingly helpful!!

[@Eigensteve]

Glad it helped!

[@19f191ty]

Thank you Steve for this brilliant video. It would be really nice if at some point you can compare and contrast various approaches of taking derivatives on real, noisy data. Almost everyone I know has their own favorite way of computing derivatives from data, and there seems to be very little I can find out there about the merit of all the different techniques. Finite difference, polynomial filtering, fft based with different choice of filters, total variational regularization, svd, orthogonal polynomials, and more. Each of these methods comes with parameters, which practioners seem to chooses by "feel". It would be nice if you could shine light on this in a future video. I think I would sleep better at night knowing how to comput derivatives from my data correctly, or understanding why I can't and what's the best I can do.

[@5JAAB]

Wow. I've never thought about making derivatives by using the FFT. Great job. Thanks a lot.

[@MaksymCzech]

Thank you man, we live in a society!

[@VauRDeC]

Lenin would have loved what's happening here xD

[@mostafapirasteh5810]

thank you Steve, your Fourier Analysis series is really helpful and valuable for me

[@lernenmitrobin]

Nice explanation, never thought about using the fft to calc the derivatives. But when I think about: It's obvious, that's a more precise method comparing to difference quotient method.

[@ahmadalghooneh2105]

Thank you Steve, the best material with the best teaching as always. Just I have two questions: 1- The reason that inverse Fourier transform results in complex values could be sometimes a non-hermitian spectrum or as you said bad computations. Since you have already done some operations on the spectrum, it may cause the spectrum to not be hermitian anymore. Taking the real part of the inverse Fourier transform could really cause serious damages to signal, especially if we are dealing with speeches and images. Am I right? if yes what could we do to make the spectrum hermitian again without loss of information? 2- How much this approach helps when having noisy data? Thank you again so much for your videos.

[@Eigensteve]

Great questions. Yes, you are right -- in practice, we should be more careful about modifying the spectrum and then iFFT'ing. There are whole textbooks on filtering and how to do this carefully. But for a simple illustration, usually this works pretty well. This approach is pretty good at filtering noisy data. The last couple of videos were specifically about how to filter noisy data using the FFT.

[@bipedalnarwhal277]

Worked perfectly, thank you!!

[@AshrafElDroubi]

Loving this series! Thank you Steve! Will there be more videos coming out soon?

[@Eigensteve]

Awesome thanks! Yes, new videos every week.

[@juandavidnavarro]

Steve, It would be interesting to compare spectral differentiation with the complex-step differentiation

[@akanguven114]

Sir what is your MATLAB coding text font? It looks pretty cool. Amazing course, Thank You!

[@theBlaxicindasian]

Very cool method for computing a derivative in post processing. Is there some way that this could be used for control? My first thought is to have a sensor sampling rate which is 2^n times a control loop frequency, fill a buffer with 2^n samples, and use that to compute a derivative which will be fed to the controller at each timestep. For the purposes of control would it be better to just use a finite difference with some filtering?

[@mphysiker]

Nice lecture

[@behnamkazemimajd8825]

hi thanks for the great tutorial ! im new to fft and dont know a lot. im trying to caculate the derivative of series of data points that are distributed non-uniformly. how can i define a vector of frequencies for non-uniform grid ?

[@alexeyl22]

Would be nice to see this in Python. With Gibbs phenomenon showing, what is cutoff frequency in IFFT?

[@Eigensteve]

Here it is in Python: kzbin.info/www/bejne/r2m2op6gpLCJas0 Most codes are in Matlab and Python (check databookuw.com)

[@akshayvishwakarma]

great explanation !!!

[@manfredbogner9799]

Very good

[@adaptine]

Is this way of computing the derivative useable in a real-time application? For instance in a PID controller?

[@mohammadalfandi1946]

excusme sir, i want to talk about thecnically how to make this video, you make a other plugin then stream with encoder or you make a program thats make this video can be write blind the screen capture? thanks very much i hope that answered immediately. :)

[@vitormateusmartini3946]

I had a computational test yesterday and the professor asked for the derivative of a function using fft and ifft. Now I found out that I should've used fftshift to re-arrange the omega vector... Oh my :(

[@ankitchatterjee5343]

Sir can you help me out with one thing? How to solve ode in matlab that involves 2 dimensions i.e where x belongz to R2

[@제갈식]

I met this error when run matlab code, " 'end' variable is not define" ...what's wrong to me ?

[@Eigensteve]

"end" should end either a loop (like for, while) or an if statement. It sounds like maybe you have an extra "end" somewhere?

[@akshayvishwakarma]

when I initiate x (line no 6) as x= 0:dx:L instead of x=-L/2:dx"L/2-dx; my calculations show erroneous result !!!

[@wuhuipwn]

How can I make my Matlab look like this?