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

Sdílet
Vložit
  • čas přidán 22. 02. 2021
  • 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

Komentáře • 86

  • @rayday4644
    @rayday4644 Před 3 lety +45

    3Blue1brown now has a competition 😎

  • @DiiaBloodyRain
    @DiiaBloodyRain Před 7 měsíci +21

    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 Před 23 dny

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

  • @Molaga
    @Molaga Před 2 lety +14

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

  • @Tennis2016
    @Tennis2016 Před 3 měsíci +4

    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 !!

  • @borian1981
    @borian1981 Před 2 měsíci +2

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

  • @tiffanytoulouse229
    @tiffanytoulouse229 Před 5 měsíci +4

    best FT explanation and visualization ever met

  • @tcnoz5842
    @tcnoz5842 Před 2 měsíci

    The best ever.

  • @Simchen
    @Simchen Před měsícem +1

    This was immensely informative

  • @Tennis2016
    @Tennis2016 Před 3 měsíci +1

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

  • @cledieu
    @cledieu Před měsícem

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

  • @user-zz6qp5fl7g
    @user-zz6qp5fl7g Před 16 dny

    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 ...

  • @Francesco_Luligo
    @Francesco_Luligo Před 9 měsíci +2

    This is a piece of art

  • @ananthchandra7792
    @ananthchandra7792 Před 4 měsíci

    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.

  • @djredrover
    @djredrover Před 9 měsíci +1

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

  • @mario1ua
    @mario1ua Před 5 měsíci +1

    Just WOW!!!

  • @pauldokter2725
    @pauldokter2725 Před 6 měsíci +1

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

  • @yolamontalvan9502
    @yolamontalvan9502 Před 5 měsíci +1

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

  • @mnada72
    @mnada72 Před 10 měsíci +2

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

  • @fantastic_n0b
    @fantastic_n0b Před měsícem

    Man the prism analogy really hit me hard

  • @RDayan932
    @RDayan932 Před 3 lety +1

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

  • @white-anthony
    @white-anthony Před 7 měsíci +1

    This is amazing, please make more.

  • @JosephParker7
    @JosephParker7 Před 2 měsíci

    Work of art

  • @gokulakrishnan3769
    @gokulakrishnan3769 Před 6 měsíci

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

  • @Tech-mx3yp
    @Tech-mx3yp Před 11 měsíci

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

  • @agrajyadav2951
    @agrajyadav2951 Před 6 měsíci

    Wonderfully explained!

  • @sirousmohseni4
    @sirousmohseni4 Před 5 měsíci

    Great video.
    Thanks for making it.

  • @oraz.
    @oraz. Před 3 lety +1

    Awesome!

  • @sandunsiriwardena3881
    @sandunsiriwardena3881 Před 2 měsíci

    A superb presentation

  • @bkhoo5
    @bkhoo5 Před 5 měsíci

    Bravo, great job done. Thx

  • @TheJara123
    @TheJara123 Před rokem

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

  • @yf1177
    @yf1177 Před 29 dny

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

  • @putskan
    @putskan Před 7 měsíci

    Great one, thanks!

  • @khaledelsayed3507
    @khaledelsayed3507 Před 5 měsíci

    Awesome ❤

  • @userfky
    @userfky Před 2 měsíci

    Fabulous vedio!!

  • @wangjack9641
    @wangjack9641 Před 7 měsíci

    very good ...thanks

  • @TheJara123
    @TheJara123 Před rokem

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

  • @johndunn5272
    @johndunn5272 Před rokem

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

  • @momindox
    @momindox Před 3 lety

    🔥🔥🔥 Yo niiice keep it up

  • @Md.NasifIslam
    @Md.NasifIslam Před 7 dny

    How come you have only 2k subscribers?!

  • @manfredbogner9799
    @manfredbogner9799 Před 5 měsíci

    Very good

  • @Troinik
    @Troinik Před 3 měsíci

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

  • @paulgillespie4908
    @paulgillespie4908 Před 10 měsíci

    Super stufffff

  • @abhishekshrivastava2889

    U r better than 3blue1brown

  • @muhammadnajmirameli9498

    Came from reddit, good job sir!

  • @paulmendoza9736
    @paulmendoza9736 Před rokem

    Thank you!

  • @daslolo
    @daslolo Před 3 měsíci

    damn i slept so good

  • @ebnsina873
    @ebnsina873 Před 6 měsíci

    thanks dude this is very heplful

  • @govamurali2309
    @govamurali2309 Před 3 lety +1

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

  • @salimbenchekroun7543
    @salimbenchekroun7543 Před 3 lety +3

    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  Před 3 lety +1

      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.

  • @speedsystem4582
    @speedsystem4582 Před 24 dny

    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...

  • @agrajyadav2951
    @agrajyadav2951 Před 6 měsíci

    thanks a lot

  • @Sir_mostarda
    @Sir_mostarda Před 3 lety +1

    Awesome video! Keep going

  • @JohnDlugosz
    @JohnDlugosz Před rokem

    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.

  • @NadeemALZayed-ed3cz
    @NadeemALZayed-ed3cz Před 9 dny

    ♻️

  • @drfaridonamdjadi7516
    @drfaridonamdjadi7516 Před 5 měsíci

    Good video but inequality 0>t

  • @brianbeast5252
    @brianbeast5252 Před 3 lety +2

    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  Před 3 lety

      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 Před 3 lety

      @@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 Před 3 lety +2

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

    • @TheoryOfControl
      @TheoryOfControl  Před 3 lety

      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.
      czcams.com/video/acAw5WGtzuk/video.html

  • @Upendra3737
    @Upendra3737 Před 7 měsíci

    Great lecture

  • @MaheshPatel-nk9fg
    @MaheshPatel-nk9fg Před 5 měsíci

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

  • @Nick2011881
    @Nick2011881 Před 6 měsíci

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

  • @noumenon7495
    @noumenon7495 Před 7 měsíci

    Plz add Fourier photo like newton

  • @keylanoslokj1806
    @keylanoslokj1806 Před 5 měsíci

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

  • @user-fl8dy5if8s
    @user-fl8dy5if8s Před 15 dny

    Go storm regal and stone mmmoth

  • @ventriloquistmagician4735

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

  • @canadajobs2304
    @canadajobs2304 Před 3 lety +1

    What's your patreon link?

    • @TheoryOfControl
      @TheoryOfControl  Před 3 lety

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

  • @ooze9808
    @ooze9808 Před 11 měsíci

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

  • @atanjacket
    @atanjacket Před 3 lety

    Do you have a github?

  • @georgen9755
    @georgen9755 Před 5 měsíci

    Discrete

  • @wurnotantmlb
    @wurnotantmlb Před 6 měsíci

    could this have been one single bit more useful lol.

  • @aerodynamico6427
    @aerodynamico6427 Před měsícem

    Horrible. Impossible to understand.

  • @zbigniewloboda3393
    @zbigniewloboda3393 Před 23 dny

    You have no idea what you talking about.