The Fourier Series and Fourier Transform Demystified

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Creator - Jade Tan-Holmes
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Music - epidemic sound

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29 июн 2022

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Комментарии : 789

@12tone Год назад

That explanation of the Fourier Transform is probably the most intuitive I've ever heard!

@duckymomo7935 Год назад

12tone, happy to see you here

@Elenesski Год назад

@@chrisw4578 Oooo a new channel to subscribe to

@bonolio Год назад

@@Elenesski If you love Up and Atom, 3Blue1Brown will rock your world. I understood Fourier transforms, but until I watched 3Blue1Browns video on it, I didn't truly intuitively understand it. He has an amazing way of not just showing you how it works, but visualising the why in ways that really expand how you think about math.

@timandersen8030 11 месяцев назад

@@bonolio I still prefer this video over Grant's because he makes it more complicated to understand.

@ahadamin7361 4 месяца назад

True

@ohnonomorenames Год назад

When ever I watch one of Jade's videos i feel like I am watching and adult version of Playschool (an Australian kids educational TV show) there is a level of enthusiasm and 'you can do this' that comes through that is so wonderful. I often get lulled into a false sense of security and zone out and then have to go back and re-watch remembering that I'm not quite as smart as she makes me feel. Jade I love everything about the way that you do what you do it must take a mountain of work so thank you so much.

@earthling_parth Год назад

Finally!!! This was my Eureka moment. I've studied Fourier Series and Transformation multiple times during my bachelor's and masters in computer science and each time I only learned the technique and not _why_ and _how_ it's used. This is the best explanation and intuitive explanation of Fourier Series and Transformation I've ever encountered. Thank you so much Jade! You must've researched really hard to come up with the examples and simpler words to explain this. Thank you once again ♥️

@starfishandroid Месяц назад

Same. Music producer here. This was my eureka moment.

@Dixavd Год назад

You've become such an amazing educational video creator, Jade! The cinematography amazing: lighting, camera quality, colour-correction, framing, pacing,, etc... You've even mastered how to use these skills to effectively get your point across without it becoming a distraction. I supported you on patreon previously but had to stop for financial reasons and I then didn't keep up with your uploads (mostly because my physics studies became so exhausting, I rarely had the energy to watch physics videos for fun). I'm so glad I looked you up again, though. I'm very proud of how far you've come. Keep it up.

@lvmbk3755 Год назад

Being a telecommunication engineer I perfectly know how Fourier transforms are ubiquitous, as they are necessary for signal processing an electronic communications. But it is fundamental also for buildings and mechanics because the analysis in the frequency domain allows to understand how materials and systems behave under given inputs. I think nowadays it is as essential as basic math operators like +, -, /, *, etc....

@markawbolton Год назад

It is also very beautiful.

@daviskipchirchir1357 Год назад

Just got introduced into Fourier Series and transforms. My mind is still blown up tbh

@Jadstudio7 Год назад

I concur

@mastershooter64 8 месяцев назад

Integral transforms in general are absolutely ubiquitous. Functional analysis is beautiful

@festusajayi8917 7 месяцев назад

Engineering mathematics is core course for all engineers irrespective of the discipline of engineering. Fourier Series is covered in details in engineering mathematics

@trewaldo Год назад

This is my most favorite topic in introductory signal processing where signals in the time domain exhibit a certain characteristic in the frequency domain through respective spectral properties. Thanks, Jade, for the animated and colorful video! Cheers! 😍🤓🥰

@jasonfairbanks4714 10 дней назад

OMG! You just taught me more about this topic in 15 minutes than my college professor spent 4+ weeks doing and failed. Where have you been all my life! Thank you!

@SKULDROPR Год назад

This concept blew my mind the first time I learned about it at uni. Until then, I had never realised, or even considered you could transform from one domain to another. I'm now an audio engineer, it's astonishing how ubiquitous, useful and practical the Fourier transform is in the field. I liked the tie in to real world algorithms at the end. I would like to see a video about different sorting algorithms if possible! My personal favourite is the radix sort.

@hackerguitar Год назад

Isomorphism for the win! it shows up everywhere….I’ve been seeing it more and more in speech recognition algorithms.

@averagejoebitcoin Год назад

linear algebra. that change of basis vectors and yet still able to Span the entire space "=" sinx and cosx can span the entire "function space"

@kpriya4739 11 месяцев назад

Hi I also aim to become an audio engineer. Can you please share your contact details if you are interested in guiding me? Please I have a few queries.

@kingbeauregard 11 месяцев назад

Calculus in general does that, when you think about it. Like with simple kinematics: you can describe an object's motion in terms of position, or take the derivative to describe that same motion in terms of velocity, or take the derivative one more time to describe that same motion in terms of acceleration.

@BleuSquid Год назад

My favourite usage, and indeed my introduction to, the Fourier Transform is in Mersenne primality testing. The most computationally expensive part of some primality tests is a squaring of a very large integer. By representing the digits of the number as time-series array, taking the fourier transform, squaring the individual elements (this step can be done massively parallel, hello GPU computing!), and then transforming it back, we have effectively squared the original number in a fraction of the time.

@ehrichweiss Год назад

I've always love the Fourier transform. I first learned of it back in the early 1990s when I was using a "granular synthesizer" that would let you draw a picture and then it'd convert that into sound. It took over 20 years for some software to duplicate that synthesizer. BTW, my wife and I bought your t-shirts and we love them. Keep up the good work.

@henryukagwu5183 Год назад

That's wonderful

@deang5622 Год назад

Fairlight music synthesizer had this capability in 1979.

@divitrajgogia4909 2 месяца назад

The best video on RU-vid for Fourier transform and analysis! Please make more videos on this part of physics/ engineering. This feeling of understanding and visualization of Fourier transforms is extremely satisfying! Thanks for making a great video.

@no_justno 4 месяца назад

Your editing is PHENOMENAL. Also this is the best explanation.

@shaovoon 2 месяца назад

I wish I had a teacher like Jade when I learned the Fourier Transform 20+ years ago. Thanks for the brilliant explanation and superb animations that helped me understand!

@adsbhushan5123 Год назад

Thanks for cracking open a black box, I've been carrying since college physics. Brilliant exposition and the accompanying video makes it easier to understand.

@AaronJarecki Год назад

I've come across these concepts before. What I love about this video, and many of your other videos, is that you encouraged the viewer to go beyond understanding that this works and explained how it worked. Super impressed with this explanation. Thanks Jade!

@bitsandbytes1s0s Год назад

This is in my math curriculum and i was soo obsessed by them, thanks for this video

@denkenunddanken5961 Год назад

Me too was so much obssed with this in my 2nd year college.

@daviskipchirchir1357 Год назад

It's my second year of college right now I'm so obsessed with this😂😂😂😂 The Fourier of being obsessed at 2nd year correlates with these three souls💀😂

@denkenunddanken5961 Год назад

@@daviskipchirchir1357 🤣🤣🤣 cool

@vector8310 Год назад

Your explanations are models of clarity. Just the right amounts of illustration and conceptual elaboration.

@johnydyroy1576 Год назад

I'm so impressed, easy and understandable explications and great animations! Keep up the good work!

@vctor611 Год назад

Amazing video Jade! I learned so much! Definitely needed something like this!

@rohank9292 Год назад

so may years spent trying to understand fourier series and transform and then this one 14 minute long video comes along and makes things all so clear. Thank you

@vsalt69 Год назад

I really appreciate the way you focused on the real number amplitude components as a way of simplifying your lesson. Not worrying about phase allows you to clearly show the connection between the integral calculations and its amplitude spectrum. This was the clearest of dozens of explanations I've read and watched over the last 20 years. Thank you so much.

@johnshioli1499 Год назад

I’m always excited to see a new UaA video come in, and this one didn’t disappoint! Fourier transforms always seemed like magic to me, but your explanation made it all make sense. Also, beautiful locations! That mountain and lake (river?) scene was gorgeous! 👏

@triberium_ Год назад

Very interesting, thank you! I'm working on a video game and waves are great for generating terrain and this has given me more tools to use with the world generation part of it all

@animalbliss3713 Год назад

You are amazing at explaining hard topics. Keep up the great work!❤️

@adamharris6557 Год назад

Great explanation and graphics. Of all the videos on this topic, your explanation is the most intuitive. You break down everything and explain each piece of the puzzle with great graphics. I'm recommending all my students to this video from now on.

@adolfos1991 Год назад

Thanks Jade for another awesome video!! I wish our lecturers were as good as you when it comes to explaining complex subjects with such simplicity.

@facundomazzola7115 3 месяца назад

loved the video. the editing and visual effects were amazing!!

@loberd09 Год назад

Thanks for the video. I’ve been a chemist in industry for 15 years. I learned it back in college but wasn’t great with it. I’ve had to “black box” it (use without a firm understanding) in explanations for instrumentation I use (FT-IR) and some instrument designs I’ve worked on. This is a great explanation. Not sure it’s a refresher for me as I wasn’t solid on it when I learned it.

@markgoodall1388 Год назад

I was thinking the same thing actually, but watching this I do wonder if the technique is under utilised in the chemistry domain.

@JohnSmith-qp4bt Год назад

But do you really need to understand the mathematical basis? And not rather focus on identification? Are you still working in the lab after 15 years in the chemical industry??? Not a department manager or director by now?

@markgoodall1388 Год назад

@@JohnSmith-qp4bt so many assumptions! Having some level of understanding would seem essential actually. I suggested that the technique was underutilised, meaning I ponder the possibility of using FT outside of the domain of FTIR. Maybe it already is? I mean, I did stop worli in laboratories over 20 years ago. So, yeah, I was just musing. Feel free to now take a dig about not being 'current'. lol

@user-ee7sc1nu6n 11 месяцев назад

@@markgoodall1388😊

@balasubramanianvaidyalinga487 8 месяцев назад

Thanks! Possibly the clearest intro to the topic. Sharing this with my kid. Subscribed as well.❤

@DeepakGautamX Год назад

Fourier transform, this is interesting. I have studied it my graduation. This could use in various cool projects.

@yasscat5484 Год назад

1:04 you mean a higher frequency* great explanation exactly when I needed it

@legendrams548 Год назад

This is a superb explanation of Fourier Series and Fourier Transformation. Loved the way you presented this entire video. Highly informative! Thanks a lot to you!👍👍

@brunotrotti6942 Год назад

Very good the way it mixed up the intuitive and simple explanation about the matter with the maths jargoons and formalism. Connected different subjects and captured the hole picture in awesome way. Really congrats

@shunpinhsu Год назад

Fourier series works mainly on `periodic' functions. Aperiodic functions are treated as periodic functions with their periods tending to infinity. In this case, the Fourier series (in the form of summation) takes the form of integration, which is known as the Foruier transform.

@AmitKumar-xw5gp Год назад

Very very well explained. Love the way you explain the topics.. You have a gift to be able to explain a concept in a simple way.. Keep making videos..

@AMANKUMAR-oh1zt Год назад

Reminds of 2nd Year in College. Had a course in Signal Processing and my overall B.Tech. in Electrical Engineering. Fourier series is indeed freaking stuff.

@fiNitEarth Год назад

This video is FANTASTIC! I've been using the Fourier transform in data science a lot and thought I had a pretty good understanding of the matter. This video however gave me a whole new intuition for it. By far the best video on Fourier I've ever seen!!

@bonolio Год назад

If you haven't watched 3Blue1Browns videos then I would suggest. I won't say they are better or worse, but he comes at the intuitive understanding from a different angle. The more ways you can visualise how something works, the better you can intuitively form solutions

@daviskipchirchir1357 Год назад

Hello how do you use Fourier transform in data science?

@mitchwyatt9230 Год назад

Around the 12 min mark, The orthogonality was glossed over a bit here, but it's an important point - the orthogonality is what keeps the calculations for decomposition into component sin and cos waves (relatively) simple. P.S. Fantastic video overall. I really think this is my favorite yet of all your videos. Please keep up the good work!

@Flovus Год назад

Exactly. Orthogonality is not necessary to describe any vector, a basis is already sufficient. Has anyone ever tried non-orthogonal bases for Fourier-related transforms?

@Shahzaib.Haider Год назад

You made my Day!!! A lot of doubts related to the Fourier Series are eleminated. Now, SIGNALS AND SYSTEMS is a fantastic subject for me. Thank You so much,

@harshans7712 Месяц назад

This video has one of the best explanation for Fourier Series along with it's application, these types of videos really intrigue every learner about this topic and make them fall in love with the subject, really hats off to your effort 🙌

@GarryMah85 Год назад

Fourier transform was a topic I could never understood during my undergraduate studies almost 2 decades ago. I'd always skipped any Math examination question that require us to use Fourier transform. While I still doubt I'll ever be able to comprehend the mathematical part of it, your video actually gave me a great idea of what Fourier series and Fourier transform is all about. Thank you. I wished we had resources like this 20 years ago, lol. It helps make sense of all the abstract mathematical concepts we had to learn.

@abirsadhu5538 Год назад

Also you can check fourier series and fourier transform video in 3blue1brown channel. They are amazing.

@sparky7915 Год назад

Great video! I never heard of Fourier series and transforms. Quite interesting! You make the complicated things easier to understand. I love watching videos on this channel because I am always learning something.

@briansauk6837 Год назад

Great video! One neat trick to solve for series is to consider the derivative or integral of a series that is easier to find. For example, once you have the square wave series, you can trivially solve for a triangle wave, by doing the simple integral of each sin term. That’s because a triangle wave is the integral of a square wave.

@jannickharambe8550 Год назад

I love you so much! The way you explain things is breathtaking! You take complicated topics and explain them so easily with simple words - Richard Feynman would be proud of you, that's for sure! Myself, I want to thank you. You help me understand a lot of things that I will be needing/need for my studies. And it's so much fun to watch your videos!

@cw9249 Год назад

beautiful visual explanation!! well done

@Pingviinimursu Год назад

I could have used a high-quality video like this to explain some of this stuff when I studied them, the visualization is a lot better than the ones I saw. I'm happy this video exists now, so others might find it useful and who knows, I might come back to this stuff some day as well :) Thank you Jade!

@tinhoyhu Год назад

Thanks for the video. This really brings me back to 30 years ago during a nerdy summer program where I had a project to modify sound recordings using FFT.

@FrederickStadler Год назад

Great job with this video, Up and Atom. I thought the material was very interesting and well explained. Keep up the great work!

@xaviergonzalez5828 2 месяца назад

It's one of the best videos about Fourier transformation. Thanks!

@jadermcs Год назад

The video editing is improving a lot, really liked the editing of this video.

@ivanliptak19 Год назад

Thank you for taking on this topic! I find it wildly fascinating, as with acoustics generally.

@wozzlebaby5313 11 месяцев назад

Wow. By far the best and most thorough explanation of this topic I have ever seen.

@baljeetin581 Год назад

Love you jade, just found you today. Feels good. I am a computer programmer. Your videos seem very helpful to me. Your presentation seem so natural. I do believe to work with your concepts. 😃

@tedblack2288 8 месяцев назад

Nicely done, Jade. I was introduced to, and began using Fourier Transforms in the 1970's. One of the things I learned is that one does not need the basis vectors to be orthogonal provided they are non-degenerate. As long as each basis vector cannot be described in terms of any other basis in the set, one can still get an absolute description of the phenomenon! When one is examining Complex space, this trick can sometimes massively increase the number of signals that are actually observed. (fyi, Real life detectors simply cannot see spectral lines that have a non-zero imaginary component.) This technique was used to double the observables in early MRI spectra.

@legosteveb 11 месяцев назад

OMG 10:31 blew my mind! Thinking about the integral as a correlation calculation is the most concise description of FFT I ever heard! Amazing how similar this is to brute force image correlation. Thanks for demystifying the often labeled “magic“ FFT function.

@borisnges4285 10 месяцев назад

Thanks, I watched your video just for a few minutes and it cleared a lot of doubts I had concerning Fourier. Thank you

@DarylBanttari Год назад

The graphic at 5:50 blew my MIND. SO MANY CONNECTIONS. Gonna have to dive into this harder now that it's not just a magic black box. Your videos are amazing, keep it up!

@rkamalat 2 месяца назад

Wonderful way of explaining Fourier Series and Fourier transform. Have taken a few of your diagrams for my lectures on DSP. Thank You so much.

@albertopacheco2244 Год назад

Very simple explanation of a very abstract topic. You have a gift.

@mr.nobody.01 Год назад

You know so much how to explain complicated things to us. Thank you and keep going.

@anantaacharya3019 Год назад

Fantastic presentation, you have made it so interesting, giving a very good concept, really enjoyed.

@alangaha1869 Год назад

Great Video Jade, thank you. A clear and concise explanation, well presented. I wish I had been able to see this 30 years ago before university.

@numericalcode Год назад

Superior explanation and visuals. Well done!

@IntegralDeLinha Год назад

What a coincidence. I was really needing a video about this right now. Thank you!

@jimdevilbiss9125 Год назад

It is great to see this being shown. The best part of my electronic engineering college was Fourier analysis.

@anthonydefreitas1694 Год назад

You always have the absolute best videos!!!! Because of you I read about physics all the time now. Was obsessed with history and politics and rarely go back now. You make these topics so much more interesting. Wish i was better at math. School made it seem so lame

@EdwinaTS 2 месяца назад

Fantastic way of seeing the transform. Many thanks!

@NolanManteufel Год назад

Love the video. Thanks for posting!

@zach4505 Год назад

A well made video. Thank you for adding some intuition to the formulas.

@mathwithmurghoobahmedsyed7112 10 месяцев назад

Excellent explanation, what a remarkable effort to explain the concept , may you have million views and subscribers

@kaemmili4590 Год назад

that was a masterclass in teaching and clarity . would have loved more details and slower pace , but rewatching and google will work , thank you so much

@andrewv.157 Год назад

I did not remember of all of this. It was a pleasure to be taught again quick and gracefully

@blueckaym Год назад

Fourier series & transform are incredibly powerful instrument that can be used in most of our aspects of life. While it's actually not perfect - as it doesn't provide the best possible solution (unless you're ok with applying more and more sine-waves to infinity) it's surprisingly powerful in practical terms. One (of the many) curious things about it, is that it's in the core of Heisenberg Uncertainty Principle (HUP). That's can be very confusing to most people, as most think that HUP is actually related to something physical in the nature of the quantum particles (I thought so too until not long ago) and one of the most popular explanations is that you can't measure a property of a quantum particle w/o interacting with it and affect its other properties in doing so. But this isn't at the core of the problem - it's a practical measuring problem (that we might not ever be able to solve), but doesn't actually say much about the nature of the quantum particles - ie what they do while we're NOT observing them. ... anyway the solution to this problem is still a mystery, and we might never find it (many scientists have already given up, and prefer to "shut up and calculate" what they can), but the current truth about HUP is that physicists are using Fourier series & transform as a tool for their measurements and the uncertainty is actually embedded in the HUP itself - it's a limitation of our Math Tool (no matter that it's indeed really, really powerful otherwise)! It's not necessary limitation of the universe (at quantum level)! That's pretty much the same question - Did we discover Math or did we invent it? - but with quantum physics seasoning :) While in most cases it's not practical to wonder about the philosophical aspect of a given field of science, it's extremely important imho that it's never ignored completely, as most people start to believe that what Math is telling us is what Universe actually IS ... which might be the case sometimes, but isn't really necessary true. Math is like a keyhole and if we sometimes see things take keyhole-shape (as we're looking thru it) doesn't mean that we're seeing the whole picture and that it's indeed their real shape.

@nadirnoorzai7753 Год назад

presentation and presenter are both just wonderful. Very well done, love it.

@manurajbharall 5 месяцев назад

Thanks,it is one of the best way to explain Fourier

@jeremylaughery2555 4 месяца назад

Awesome video! I am using Fourier analysis to help with modeling a general prime number generator or prime number sieve. Fourier analysis is a game changer!

@travo6805 2 месяца назад

You explained this better than my professor is going to explain it on Monday, thanks

@alihuzaifa235 Год назад

In all i just want to say thank you so much for making such an amazing concept an understandable one, i love that....

@swanronson173 Год назад

Great stuff as always Jade 👍

@mustafizurrahman5699 2 месяца назад

Simply splendid. Love ❤️ such exploration

@mogaon9489 Год назад

Thanks,You make the complex understandable and fun

@vsr600 Год назад

I am an expert in using the FFT, a PhD acoustics physicist here... and I for some reason never thought of it as a cross correlation of your signal with e^-iwt. Makes total sense now. That was great, I learned something. Thanks!

@Flaschenente Год назад

Great explanation! Thank you for this great video

@briancox2721 Год назад

You can't write any function as a sum of sin functions, only periodic ones which repeat. For example, f(x)=x never repeats, and so has no frequency component to produce by summing sin waves.

@thegzak Год назад

As usual, great job giving an intuition to complex topics - as Walter Lewin would say, you’re getting people “to see through the equations.” Bravo!

@clavierwintergreen5574 3 месяца назад

Fantastic video 👏🏼👏🏼👏🏼 Could you make a video explaining (or demystifying) the Laplace transform as well?

@curtpiazza1688 Год назад

Beautiful intro. to Fourier Series! Very well explained and presented! Lots of applications to music!

@raghodsa 8 месяцев назад

Brilliant yet simple explanation! Thank you for your efforts👏🏻

@user-if7kr5yu3n 28 дней назад

That is a very nice, informative and easier explanation. Thank you very much... ❤❤❤

@denkenunddanken5961 Год назад

I was waiting for your vedios and for last few days I was looking at your channel for new vedio. And here you comes with a topic i loved so much during my college studies. 🙏🙏 God bless u

@carlmakafui Год назад

Thanks for explaining it so clearly. Amazing content!

@elmo2you Год назад

Great video and it certainly will help to get a better or more intuitive understanding of Fourier Series and its Transform function. One thing I would like to add though, is that is isn't just a tool. It also has a very real-word importance in (physical) systems. Whenever a transient signal travels through a system, its ability to propagate or sustain itself will depend on how that system responds to it. In physical systems, electronics being a particular important one, signals with different frequencies will face a different resistance/impedance. Those who ever watched a high-frequency digital square wave on an oscilloscope may have noticed that it wasn't quite square. Instead having oscillations around each vertical rise and fall of the signal, similar to the reconstructed square and saw-tooth waveform in this video's animations. This is because real-life systems (including measuring equipment) have a specific frequency response (and often a different one for each individual frequency). Specifically in electronics, sufficiently high frequencies won't make it through a system (often because the physics of the system can't keep up with the rate of change). It is these high frequency components in a Fourier Series that enable signal to have sharp corners (rapid non-gradual changes). That is what makes an ideal square or saw-tooth wave (or essentially anything with sharp corners on a time-graph) impossible to exist/survive in a real-life (electronics) system. It is not just that the Fourier Series and Transform are useful tools, it is also the relationship between transient signals and their frequency components that determines how they will propagate through real-life systems. While I took electronics as an example, there are plenty of other systems for which the same principle hold.

@timandersen8030 11 месяцев назад

How does Fourier transform work if you don't have an input function but only raw signal/sound wave as in real world scenario?

@michaelmartin8337 Год назад

Wonderfully informative video Jade Thank you😁

@samarpanbiswas7474 Год назад

Jade, loved it, dear. You smashed it as always

@glengineertv1505 Год назад

I have worked with an spectrum analyzer arduino code library before. I now understand why the algorithm is multiplying data to a series of numbers which seems correspond to a sine wave. Very good video! Keep it up! Thank you 😊

@rsssl Месяц назад

After watching numerous videos; I finally understood this one. Thank you.

@meow75714 8 месяцев назад

Although I know about Fourier series and transforms and have been using it for a few years, this video still added to the basic foundational understanding of it. Much love 💟