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

Theory Of Control
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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:
---------------------------------------
Twitter: / theoryofcontrol​
Facebook: / theoryofcontrol​
Background Music:
What Happens Then - Kikoru
#Manim​
#DSP​
#Fourier

Опубликовано:

 

22 фев 2021

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Комментарии : 89   
@rayday4644
@rayday4644 3 года назад
3Blue1brown now has a competition 😎
@Tennis2016
@Tennis2016 4 месяца назад
This video is even better !!
@thisukainol
@thisukainol 3 месяца назад
@@Tennis2016 yepp
@DiiaBloodyRain
@DiiaBloodyRain 8 месяцев назад
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
@gulamm1 Месяц назад
Fully agree. Excellent explanation with color graphics but background music, for me, kind of annoying.
@prashantvishwakarma2091
@prashantvishwakarma2091 16 дней назад
Great Explanation. Thank you very much
@Molaga
@Molaga 2 года назад
A stunning presentation. Technically rigorous. It has everything I want to know or say about Fourier Transform. Thanks -infinity to +infinity :)
@borian1981
@borian1981 3 месяца назад
I studied this stuff on 2004,before all those RU-vid videos were available. Now,it's much more easy to understand Thank u for such clear explanation
@Tennis2016
@Tennis2016 4 месяца назад
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 !!
@tiffanytoulouse229
@tiffanytoulouse229 6 месяцев назад
best FT explanation and visualization ever met
@cledieu
@cledieu 2 месяца назад
You have convoluted art and science. Congratulations for this amazing piece of work.
@ananthchandra7792
@ananthchandra7792 5 месяцев назад
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.
@Tennis2016
@Tennis2016 4 месяца назад
This is such an amazing video : best Fourier Series/Transform video 💎 … and I have watch all top science channels on this topic before 👏👏👏
@RDayan932
@RDayan932 3 года назад
Thank you for putting this out, can't wait to see more videos from you on this topic in the near (hopefully) future.
@Simchen
@Simchen 2 месяца назад
This was immensely informative
@Francesco_Luligo
@Francesco_Luligo 10 месяцев назад
This is a piece of art
@djredrover
@djredrover 10 месяцев назад
Great video! Grant's Manim library is all over youtube!
@userfky
@userfky 3 месяца назад
Fabulous vedio!!
@user-zz6qp5fl7g
@user-zz6qp5fl7g Месяц назад
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
@gokulakrishnan3769 7 месяцев назад
Thank you for the wonderful explanation! Great work🎉 waiting for your new updates.
@mnada72
@mnada72 11 месяцев назад
Thank you. You have explained it clearly. Very good luck with the rest of control theory topics. Waiting for the same for Laplace transform.
@white-anthony
@white-anthony 8 месяцев назад
This is amazing, please make more.
@agrajyadav2951
@agrajyadav2951 7 месяцев назад
Wonderfully explained!
@sirousmohseni4
@sirousmohseni4 6 месяцев назад
Great video. Thanks for making it.
@pauldokter2725
@pauldokter2725 7 месяцев назад
What a beautiful brain boom. Thank you. I have been mystified by this for too long.
@bkhoo5
@bkhoo5 6 месяцев назад
Bravo, great job done. Thx
@mario1ua
@mario1ua 6 месяцев назад
Just WOW!!!
@momindox
@momindox 3 года назад
🔥🔥🔥 Yo niiice keep it up
@sandunsiriwardena3881
@sandunsiriwardena3881 3 месяца назад
A superb presentation
@putskan
@putskan 8 месяцев назад
Great one, thanks!
@JosephParker7
@JosephParker7 4 месяца назад
Work of art
@wangjack9641
@wangjack9641 8 месяцев назад
very good ...thanks
@fantastic_n0b
@fantastic_n0b 2 месяца назад
Man the prism analogy really hit me hard
@oraz.
@oraz. 3 года назад
Awesome!
@johndunn5272
@johndunn5272 Год назад
Brilliant...and that's hard for me to say. Well done
@Tech-mx3yp
@Tech-mx3yp Год назад
Ahaka ingun ani diay ni! Lamia ebalik skwela. Karon pako kasabut
@TheJara123
@TheJara123 Год назад
Jesus, you got a fantastic opening analogy I ever saw on RU-vid phy. Super...
@khaledelsayed3507
@khaledelsayed3507 6 месяцев назад
Awesome ❤
@muhammadnajmirameli9498
@muhammadnajmirameli9498 3 года назад
Came from reddit, good job sir!
@paulgillespie4908
@paulgillespie4908 11 месяцев назад
Super stufffff
@yolamontalvan9502
@yolamontalvan9502 6 месяцев назад
Amazing videos with great animations. I’ll use manin to make videos to teach kids he numbers and how to count. Thanks.
@manfredbogner9799
@manfredbogner9799 6 месяцев назад
Very good
@ebnsina873
@ebnsina873 7 месяцев назад
thanks dude this is very heplful
@tcnoz5842
@tcnoz5842 3 месяца назад
The best ever.
@Troynjk
@Troynjk 4 месяца назад
Are you planning on making more videos? You’re really good at it.
@Sir_mostarda
@Sir_mostarda 3 года назад
Awesome video! Keep going
@paulmendoza9736
@paulmendoza9736 Год назад
Thank you!
@govamurali2309
@govamurali2309 3 года назад
Amazing, could you please do videos on Laplace and Z transform.
@TheJara123
@TheJara123 Год назад
Why this excellent video has so few views?? Tube algorithm gone rogue? ..
@yf1177
@yf1177 2 месяца назад
Fantastic video! 6:55 ('here is our FFT' or did you mean to say 'signal'?)
@salimbenchekroun7543
@salimbenchekroun7543 3 года назад
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
@TheoryOfControl 3 года назад
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
@agrajyadav2951 7 месяцев назад
thanks a lot
@JohnDlugosz
@JohnDlugosz Год назад
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.
@speedsystem4582
@speedsystem4582 Месяц назад
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...
@Upendra3737
@Upendra3737 8 месяцев назад
Great lecture
@daslolo
@daslolo 4 месяца назад
damn i slept so good
@Md.NasifIslam
@Md.NasifIslam Месяц назад
How come you have only 2k subscribers?!
@brianbeast5252
@brianbeast5252 3 года назад
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
@TheoryOfControl 3 года назад
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
@brianbeast5252 3 года назад
@@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.
@canadajobs2304
@canadajobs2304 3 года назад
Don't quite get convolution at the end, especially the "land" part
@TheoryOfControl
@TheoryOfControl 3 года назад
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. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-acAw5WGtzuk.html
@abhishekshrivastava2889
@abhishekshrivastava2889 Месяц назад
U r better than 3blue1brown
@강모경
@강모경 25 дней назад
안녕하세요. 간결하고 짜임새있는 설명 감사합니다. 스마트폰 속의 수학이라는 주제의 교육용 학습 영상을 제작하려고 합니다. 자료로 참고해도 될까요? 정확한 출처 기록 후 사용하도록 하겠습니다. 감사합니다.
@drfaridonamdjadi7516
@drfaridonamdjadi7516 6 месяцев назад
Good video but inequality 0>t
@NadeemALZayed-ed3cz
@NadeemALZayed-ed3cz Месяц назад
♻️
@MaheshPatel-nk9fg
@MaheshPatel-nk9fg 6 месяцев назад
How do you create the animation? What is the name of the program ?
@noumenon7495
@noumenon7495 8 месяцев назад
Plz add Fourier photo like newton
@ventriloquistmagician4735
@ventriloquistmagician4735 3 года назад
Very good. How can I donate a few dollars? God bless you
@Nick2011881
@Nick2011881 7 месяцев назад
The circle you are drawing at 8:16 seems to be cos(wt) and not sin(wt). Are you sure its sin(wt)?
@keylanoslokj1806
@keylanoslokj1806 6 месяцев назад
Why did you stop uploading? You could be one of the top tech utubers
@themightyquinn100
@themightyquinn100 3 месяца назад
Maybe he died?
@user-fl8dy5if8s
@user-fl8dy5if8s Месяц назад
Go storm regal and stone mmmoth
@canadajobs2304
@canadajobs2304 3 года назад
What's your patreon link?
@TheoryOfControl
@TheoryOfControl 3 года назад
Thank you for pointing that our I appreciate your enthusiasm, I am working on that and will update it on the distribution very soon.
@olafgunther9401
@olafgunther9401 2 дня назад
wow, why didnt you continue??? you owe it to science for the sake of keeping new commers interested
@ooze9808
@ooze9808 Год назад
one must be slightly insane to have thought of these things, I have come to this conclusion.
@atanjacket
@atanjacket 3 года назад
Do you have a github?
@TheoryOfControl
@TheoryOfControl 3 года назад
github.com/319willy
@georgen9755
@georgen9755 6 месяцев назад
Discrete
@wurnotantmlb
@wurnotantmlb 7 месяцев назад
could this have been one single bit more useful lol.
@zbigniewloboda3393
@zbigniewloboda3393 Месяц назад
You have no idea what you talking about.
@aerodynamico6427
@aerodynamico6427 2 месяца назад
Horrible. Impossible to understand.
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