Fourier Transforms || Theoretical Interpretations, Complex Exponentials and Window Effect

First video Digital Signal Processing series. I am taking you on journey to uncover both intuitive and deep mathematical understanding of Fourier Theory.
The video cover the significance of sinusoids and complex exponentials, how to read magnitude and phase graphs, the ideal magnitude graphs and the effect of rectangular windows on the final spectrum.
Animations in this video were primarily created using #Manim the animation tool developed by @3blue1brown.
I have significant appreciations for the people online creating tutorials and illustrations of #Manim. As a part of that effort I am making all my source codes available on my GitHub page in few days after the upload.
Thank you for watching, the series will continue to more practical content on the next video. Subscribe and follow the me on social media:
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Twitter: / theoryofcontrol​
Facebook: / theoryofcontrol​
Background Music:
What Happens Then - Kikoru
#Manim​
#DSP​
#Fourier

[@rayday4644]

3Blue1brown now has a competition 😎

[@Tennis2016]

This video is even better !!

[@thisukainol]

@@Tennis2016 yepp

[@DiiaBloodyRain]

This is a jaw dropping explanation that actually reaches small-brained audience such as myself! I cannot applaud you enough for such an honest work! Thank you so much.

[@gulamm1]

Fully agree. Excellent explanation with color graphics but background music, for me, kind of annoying.

[@Tennis2016]

This video should have multi million views to render justice to the effort and intuition put on creating such a explanatory and clear content … powerful !!

[@Molaga]

A stunning presentation. Technically rigorous. It has everything I want to know or say about Fourier Transform. Thanks -infinity to +infinity :)

[@borian1981]

I studied this stuff on 2004,before all those KZbin videos were available. Now,it's much more easy to understand Thank u for such clear explanation

[@tiffanytoulouse229]

best FT explanation and visualization ever met

[@Tennis2016]

This is such an amazing video : best Fourier Series/Transform video 💎 … and I have watch all top science channels on this topic before 👏👏👏

[@cledieu]

You have convoluted art and science. Congratulations for this amazing piece of work.

[@Simchen]

This was immensely informative

[@ananthchandra7792]

Mathematical Tools & Techniques are main foundation to our modern & future technologies. Lot of Thanks to ancient & modern scholars,who develop Mathematical Technique (Trigonometry, Calculus,Probability, Algebra...etc) for solving complex problems in real time scenarios especially in field of Science,Engineering,Technology & Architecture.

[@RDayan932]

Thank you for putting this out, can't wait to see more videos from you on this topic in the near (hopefully) future.

[@pauldokter2725]

What a beautiful brain boom. Thank you. I have been mystified by this for too long.

[@Francesco_Luligo]

This is a piece of art

[@yolamontalvan9502]

Amazing videos with great animations. I’ll use manin to make videos to teach kids he numbers and how to count. Thanks.

[@mario1ua]

Just WOW!!!

[@user-zz6qp5fl7g]

Will you be coming back? I encourage you to do so. You could do a video on P.I.D. as your channel would be incomplete without it. Use real world examples: sluices on hydroelectric facilities, cruise control on cars, etc ...

[@gokulakrishnan3769]

Thank you for the wonderful explanation! Great work🎉 waiting for your new updates.

[@djredrover]

Great video! Grant's Manim library is all over youtube!

[@white-anthony]

This is amazing, please make more.

[@sirousmohseni4]

Great video. Thanks for making it.

[@bkhoo5]

Bravo, great job done. Thx

[@mnada72]

Thank you. You have explained it clearly. Very good luck with the rest of control theory topics. Waiting for the same for Laplace transform.

[@agrajyadav2951]

Wonderfully explained!

[@JosephParker7]

Work of art

[@wangjack9641]

very good ...thanks

[@tcnoz5842]

The best ever.

[@sandunsiriwardena3881]

A superb presentation

[@userfky]

Fabulous vedio!!

[@oraz.]

Awesome!

[@putskan]

Great one, thanks!

[@johndunn5272]

Brilliant...and that's hard for me to say. Well done

[@momindox]

🔥🔥🔥 Yo niiice keep it up

[@khaledelsayed3507]

Awesome ❤

[@fantastic_n0b]

Man the prism analogy really hit me hard

[@TheJara123]

Jesus, you got a fantastic opening analogy I ever saw on KZbin phy. Super...

[@manfredbogner9799]

Very good

[@paulgillespie4908]

Super stufffff

[@ebnsina873]

thanks dude this is very heplful

[@Tech-mx3yp]

Ahaka ingun ani diay ni! Lamia ebalik skwela. Karon pako kasabut

[@muhammadnajmirameli9498]

Came from reddit, good job sir!

[@paulmendoza9736]

Thank you!

[@Troinik]

Are you planning on making more videos? You’re really good at it.

[@TheJara123]

Why this excellent video has so few views?? Tube algorithm gone rogue? ..

[@govamurali2309]

Amazing, could you please do videos on Laplace and Z transform.

[@Md.NasifIslam]

How come you have only 2k subscribers?!

[@yf1177]

Fantastic video! 6:55 ('here is our FFT' or did you mean to say 'signal'?)

[@salimbenchekroun7543]

Excellent animation! I also love the new perspective brought by the explanation. Are you planning on taking a more pratical (irl examples with maybe pseudocode) or theoretical approach for the rest of the series (pun not intended)? Cheers!

[@TheoryOfControl]

Most certainly, I needed the hardcore theoretical interpretation first to land the coming practical aspects. I am planning to proceed using MATLAB and Mathematica so viewers get comfortable with Fourier transforms as a tool. Then I will progress to a vibration analysis project that puts everything into practice.

[@agrajyadav2951]

thanks a lot

[@Sir_mostarda]

Awesome video! Keep going

[@speedsystem4582]

Is it just me, or should the signal move in the opposite direction here 2:16 ? (If x-axis represent times) I really like the way you phrase some stuff, coincides and validates how I think...

[@daslolo]

damn i slept so good

[@abhishekshrivastava2889]

U r better than 3blue1brown

[@JohnDlugosz]

You should have concluded by showing how this allows the finite transform to produce meaningful results using a sweep of chosen discrete frequencies, when mathematically (using an infinite signal) only the exact frequency will produce a spike and being off by just a little bit will be zero. With the finite window, you get increasing spike as you tune into the exact frequency.

[@brianbeast5252]

this may take me a few watches to fully absorb but very interesting and well explained non the less. what do you have planned next for the series?

[@TheoryOfControl]

It’s just the beginning and I am learning so much from viewers like you about what gaps to fill. The whole purpose of this series is to practice vibration signals because I believe they can be the best practice of signal processing. I am building the foundations for that. Each highly abstract video like this one will be followed by a more elaborate simulations using software packages like Mathematica and MATLAB/SIMULINK models.

[@brianbeast5252]

@@TheoryOfControl interesting and i like the idea of boiling it down into base physics not necessarily electronics as it could be used to describe more mechanical motions. how it would connect with seismology could be interesting although im not sure how much is there or how technical that may become. definitely going the right way about this so far though, good job.

[@NadeemALZayed-ed3cz]

♻️

[@MaheshPatel-nk9fg]

How do you create the animation? What is the name of the program ?

[@canadajobs2304]

Don't quite get convolution at the end, especially the "land" part

[@TheoryOfControl]

The “landing” effect is more of an analogy than what actually happens. Think of how multiplication works on two signals, every nth sample of the first signal is multiplied by the same nth index of the second sample. If you checked the sinc function you’ll notice it’s centred around zero meaning if we multiply that by the spikes signal. Result will be zero because they are not aligned. Convolution on the other hand takes the sinc function sample by sample and slide across the spike signal, still most of the new signal is zero but when the spike matches the sinc, multiplication is non zero. Here’s a video that visually helps you see convolution in action. kzbin.info/www/bejne/l5SkqGiNfNmtq80

[@Upendra3737]

Great lecture

[@drfaridonamdjadi7516]

Good video but inequality 0>t

[@ventriloquistmagician4735]

Very good. How can I donate a few dollars? God bless you

[@noumenon7495]

Plz add Fourier photo like newton

[@Nick2011881]

The circle you are drawing at 8:16 seems to be cos(wt) and not sin(wt). Are you sure its sin(wt)?

[@keylanoslokj1806]

Why did you stop uploading? You could be one of the top tech utubers

[@themightyquinn100]

Maybe he died?

[@canadajobs2304]

What's your patreon link?

[@TheoryOfControl]

Thank you for pointing that our I appreciate your enthusiasm, I am working on that and will update it on the distribution very soon.

[@user-fl8dy5if8s]

Go storm regal and stone mmmoth

[@ooze9808]

one must be slightly insane to have thought of these things, I have come to this conclusion.

[@atanjacket]

Do you have a github?

[@TheoryOfControl]

github.com/319willy

[@georgen9755]

Discrete

[@wurnotantmlb]

could this have been one single bit more useful lol.

[@zbigniewloboda3393]

You have no idea what you talking about.

[@aerodynamico6427]

Horrible. Impossible to understand.