How to Compute a FOURIER SERIES // Formulas & Full Example

[@jlpsinde]

Oh my God, if this existed 27 years ago it would have been so much easier to learn. You are a genius teacher

[@DrTrefor]

haha I sometimes wish I could go back in time and watch my own videos:D

[@gurumayummadan2646]

@@DrTrefor haha bless you Sir

[@dj_b1627]

@@DrTrefor weird flex but ok

[@VCT3333]

Wait till you hear him teaching the better series ... Fiveier Series.!

[@LittleWhole]

@@VCT3333 I'm more of a Sixier series type of guy, but I respect your opinion

[@thegil-martingetaway8804]

There is something just so magical about when stuff like this finally clicks. Makes you feel like you've unlocked a new understanding of reality. Thank you so much Dr Trefor

[@littleKingSolomon]

If anyone asked me to show them who a teacher is, I would point to you and say Dr. Trefor Bazett. Thank you life saver and be blessed.

[@bebarshossny5148]

Can't wait for fourier transforms The way you explain things is magical

[@DrTrefor]

Me too, they are so cool!

[@samyakhp4353]

You might already know how impactful your videos are on people. But let me tell you how it helped me personally, i am from India (south), i really had a tough time getting my head around Fourier series (cuz without animation, it's very difficult to just imagine) and i can't afford to join tuitions or get paid courses for all my doubts (i am still a student), and there are hundreds of thousands of such people around the world for whom you have helped and made a difference in their learning/education. Thanks a lot 🙏🏼.

[@RobinYuan]

same here, he is a magician that made fourier series easier to understant

[@anonymous9217w2]

where in South?

[@movrew]

​@@anonymous9217w2south

[@mrinalkantidebnath1301]

Sir we are lucky that you are giving such a information for free and you teaches us what our lecturer takes 2 hour lecture to explain us , but cant explain properly.

[@anweshpanda7417]

I am able to understand this in only 10 to 15 minutes which I would take weeks to understand from books.This justifies how can a human learn faster through visuals.Thanks again for such wonderful demonstration of Fourier series

[@FitFrenzy-i4p]

I don't know anything about Fourier series yet I can understand ur video.u r doing a great job

[@young8554]

Wait a second, all this time I've been calculating Fourier series problems without knowing why. And now I Know. Thanks professor!

[@unlucky-777]

Oh my GOD you can't understand how helpful this video was I have an exam 4 days later and this saved my life thank you so much

[@crazygur1y]

I love the way you explain, you have a real gift for teaching, thanks so much!

[@Vladzag3]

Simply the best the most intuitive explanation which I was able to find. Many thanks!

[@sunsun19831206]

you are a very good teacher , your students are blessed , not even a Engineering guy explained it so well

[@inquisitiverakib5844]

1 of the best explaination. Unfortunately underrated video.

[@matthewdevis1110]

Professor, you are a national treasure. I love you

[@Kenneth-mj1hk]

You are saving my life right now. I have a DiffEq final today, and this has made it so much clearer. Thank you!

[@DrTrefor]

good luck!

[@user-qy6tu9ip9v]

Dude... fourier transforms and fourier series seems impossible to understand

[@MrLee-cy1pw]

Absolutely incredible sir. I've been out of practice for a dew years and I just picked up PDE's,so this was more than helpful. Thank you!

[@FaranAiki]

What a great video! This deserves 0 dislike (which currently is, per 05-08-2021) and many of likes!

[@elidoz9522]

this is the first time this clicked for me, thanks a lot

[@RobinYuan]

Best maths video i have ever watched, i am an electrical and electronic engineering student and when we came to communication systems the fourier series seemed to be extremely inportant but no one told me ( even in the provided reading material) the important 3 identities such as sinmtsinnt cosmtcosnt which means i would write 10 lines of equations to calculate a single coefficient! thank you Dr, youve helped me a lot with my future study.

[@HassanKhan-cs8ho]

Absolutely loved your presentation 👏 👍 😀 ❤ this made my learning so much easier and intuitive 😀

[@michaelzumpano7318]

Please do transforms too. This is the most intuitive and motivated explanation of Fourier series I’ve ever seen! Great job!

[@DrTrefor]

That's the plan!

[@user-qy6tu9ip9v]

@@DrTrefor I just don't get this stuff man... it makes me so sad.

[@prodbyKamikaZ]

Wow this clarified so much for me, all the textbooks would not do what you did by 4:30

[@HuaijinSun-ik9sg]

Fascinating video! I understand it completely

[@IntisarJabir-zj3zl]

This teacher is good, like really good and should be appreciated alot more

[@jezza10181]

Great video, thanks. Much much much better than any textbook explanation I've ever scratched my head over...

[@RitvikivtiR]

Im very drunk while watching this but I still understood, this physics degree gonna be bussin now, thanks doc!

[@philipbarthelma1903]

You're doing gods work here and I hope you know that.

[@moviemadness-omarelderiny5885]

You can choose a better analogy than that.

[@asan_fizika]

👍You explained so clearly Sir, thank you.

[@SalehGoodarzian]

Such a great explanation, thank you so much, I really got the point behind the equations. Best wishes to you

[@dovidglass5445]

Hi, thanks for this new series, I'm so excited to be learning about Fourier series! Quick question: When you were talking about the 3 important integrals, must m and n be integers?

[@DrTrefor]

Thanks! And yes, m and n are integers.

[@dovidglass5445]

@@DrTrefor Cool, thanks!

[@telodemuestro7384]

@@DrTrefor Hi, do you mean "They could be integers" or "They must be integers"? thanks for your work!

[@2001herne]

@@telodemuestro7384 They must be. If you throw it into desmos, non-integer values of m and n result in values that are not 0 or pi

[@donaldmcronald2331]

That's quite a good explanation! I learnt it through the complex exponential function but it's basically the same. You have a cos term for the even component, sine for the odd component and a constant term for the DC component. That's why your a0 term is zero in your example in your introduction.

[@weisanpang7173]

@DrTrefor, why is the integration limit set to 0 to 2pi, or -ve pi to pi ? I understand it is a period of the sine and cosine, but why is it used to compute the coefficients ?

[@user-wu8yq1rb9t]

Just *beautiful* , that's enough. Thank you Professor 💖

[@elijahidiong359]

Good work...very simplified,thanks alot

[@mohamedusaid456]

Can you discuss on Lagrangian mechanics .

[@DrTrefor]

I hope to, but going to be a bit:)

[@zacksummer9531]

you outdid 2 hours of lectures from my university in 13 minutes

[@mohamedkhalil4459]

Perfect lecture.

[@sergiolucas38]

Great explanation and editing :)

[@andrewgrebenisan6141]

You're a very talented teacher

[@peterhindes56]

The formulas at 7:00 don't seem right, they should include the period right?

[@dhawals9176]

At 2:15 shouldn't there be condition that m and n are integers?

[@darlingdarling2943]

Yes. That part through me off so bad and I was questioning things, but your comment clarified what they meant; yeah, this is only true for integer values. It’s also not true if abs(m) = abs(n) (accounting for m = -n).

[@kevinchien3878]

Super clear explanation!

[@DrTrefor]

Glad you think so!

[@moviemadness-omarelderiny5885]

Why do the cosines and sines go away when you multiply by 1

[@vahidnourmohammadi9232]

Thank you for this informative video.

[@moviemadness-omarelderiny5885]

Very helpful video

[@spideramazon5032]

For general half period L the formulas for a_n and b_n should include L as well!

[@Ankit-hc4sw]

Wish your channel existed when I was in college in the last decade :(

[@ejb7969]

At 10:07 and 12:08, you suddenly introduce an "x" into your equations. Do you mean "t" where you wrote "x"? If not, please explain where the "x" fits into this entire discussion. Many thanks!

[@osman2k]

thank you, sir, you are great!

[@thehalf-dane4907]

Hi a bit confused about the last part of the full example, aren't you only doing the integrals for the function f(x)=1 from 0 to pi? is the part where f(x)=0 from pi to 2pi not relevant? Thanks :)

[@kevthedorkslayer9848]

I am trying to understand that too its very confusing

[@MONSTERTRUCK4009]

@@kevthedorkslayer9848 From Pi to 2*Pi we're just integrating the value 0. For an indefinite integral (an integral without limits) we would write '+C' to indicate some constant. But our integral is definite (has limits Pi to 2*Pi), and the definite integral of 0 is just 0. I may be wrong in my thinking, but you could also think of "Integral = Area between the curve and the x-axis". The line f(x) = 0 is just the x-axis itself. So there is no area between them. And again, no area is just 0.

[@LysergicAsa]

you oscillate to peaks of genuine excitement and interest at a periodic rate that can I can now transform into binary to teach a robot how to effectively stimulate students... thanks

[@ShirsenduRoy-x3y]

just awesome sir!

[@theoneandonlyyoko]

in the example, what happened to the part of the function that is 0? I know you changed the integral range only to fit the value of 1, and I would guess that if you did the integral of the part 0 with its corresponding integral it would be 0, what happens if its -1?, do you do it as well? how do you add one coefficients to form one series? are they just added?

[@narendradc2402]

Very good. Thanks

[@zainabalbakaa6127]

2:41 how you could explane it in this imagen way 🥺🥺❤️

[@fixfaxerify]

1:50 Isn't this dependent on m and n being integers, which you don't specify? When I try computing for values of n that are fractions of m, very close but not equal to m, it doesn't evaluate to zero. Assuming so, that would also explain the interval from 0 to 2*pi, as you're essential looking at two multiples m and n of a base harmonic frequency of 1 and its period 2*pi. Maybe that's implied but I didn't get right away why I couldn't confirm this in mathcad for all values m and n. Otherwise great explanation.

[@saturdaymorning5222]

Great explanation

[@cuttingcut1321]

Thank you very much for the video❤️

[@DrTrefor]

You're welcome 😊

[@korakatk318]

My savior!

[@demerion]

Why are you going from 0 to 2pi instead of -pi to pi? I assume it makes no difference and it's easier to compute, but according to the general function, we need an interval [-L, L), where you can't plug in 0 and 2pi. Is this just something you can do with sin and cos? It's the same for [-pi, pi) and [0, 2pi) in this case?

[@carultch]

It's an arbitrary choice. Ultimately, you want to complete the integral over 1 full period, how ever you chose to assign it. In this particular case, it is equally as easy to integrate from 0 to 2*pi, as it is to integrate from -pi to +pi. The interval from -pi to 0, and from pi to 2*pi, both give a value of the original wave function of zero, and thus are both trivial to integrate.

[@mtssmreddy5172]

2:32 Values of m and n must be integers

[@christianmgbike6188]

Do we also write the general Fourier series for the even as well instead of only the odd fns.

[@yousifalmayyahi4462]

Well I don’t know how to say it Dr. , but i love u 😍 ❤️

[@rubberductape4985]

Hi I was wondering why do you change an and bn to am and bm. Thanks

[@chibuezendiokwelu63]

is this definite integral done from 0 to 2pi only. Why didn't you find the integral from zero to say pi/2

[@garvitmakkar]

Please make a video on how u plot these on desktop or just tell us in comments. Thanku so much U r great

[@DrTrefor]

Nothing fancy just MATLAB

[@studypurpose7804]

Thank you so much. I observed that vibration monitors record peak particle velocity with time. then there is option in the software to convert into frequency domain using Fourier transform. i have no confuse on the graph of peak particle velocity in time domain. it simply shows the sensor recording with time. if higher amplitude at 10th second, i understand there is higher vibration at 10th second in machine after starting. if i plot a graph having 10 amplitude readings from sensors with time, that may be a wave form. how can i convert into Fourier series form from the practical readings (i.e. sensor readings)? is it mandatory to form Fourier series to get frequency domain of the wave form ? Again the question, how to create Fourier series form (i.e. mathematical form) from actual vibration sensor amplitude readings? i don't know whether the question is correct or not. Thank you.

[@continnum_radhe-radhe]

This is amazing sir.... Always waiting for your new series..

[@douglas5260]

thank you for the great lecture. Can "m" be a non integer? Because the cosine plot you showed for the "m" values included points for all possible "m" continuously. But then you picked only integer values of m. Can the function be approximated with only integer frequencies? What if the function has the frequency 1.4, or 3.7 in it, for an example? Thanks

[@DrTrefor]

For now, yes, an integer. This is a discrete fourier seriers. There are other continuous options, but that is quite beyond the current scope.

[@douglas5260]

@@DrTrefor thank you.

[@aashsyed1277]

One question: the derivation in the start is for period 2π?

[@DrTrefor]

Yes

[@JovanSohi-q7y]

For a(o), why is it 1/pi instead of 1/2pi? I thought the formula was a(o) = 1/T and so on, where T is the period

[@jannik-1698]

really nice would have been nice to say that m,n have to be natural numbers for the Integral to work like that :)

[@MichaelRothwell1]

This was video was a pleasure to watch. It would have been nice if you had discussed the conditions under which we can interchange the infinite summation and integration. I guess we would need to use something like the dominated convergence theorem, with some appropriate conditions on f.

[@salvatoregiordano6816]

Such an excellent explanation! Thank you!

[@DrTrefor]

Glad it was helpful!

[@MikeNsumu]

Very good

[@br4hem_M4th]

2:08 i think these are only true if (m) and (n) are (integers) or at least it is always true in that case but not necessarily other cases

[@DrTrefor]

Yes they are implicitly assumed to be natural numbers

[@kobetutors]

This helped a lot

[@masterlearnings]

super sir beautiful explantions

[@Lexyvil]

Is a_n the same as a_m and b_n the same thing as b_m?

[@DrTrefor]

Yup just different notation

[@RobarthVideo]

Great explanation. However, is the piece wise continuity of the function and its derivative also necessary condition or is it just sufficient? I wanna go deep. Throw Lebesgue spaces at me if it is necessary.

[@shifagoyal8221]

How can u put m=0 ,when m is in denominator.

[@stefano.a]

Excellent explanation, thank you. I have an old unsolved question that perhaps you can answer: in electronics we often consider the spectrum of a signal as the “frequency content” of a signal, intended as a sum of sinusoidal functions of certain frequency. However the Fourier series describe a signal as a sum of *sine* AND *cosine* terms. How do this relate this with a spectrum of a signal?

[@andrewharrison8436]

For a specific frequency there will be, in general, sine and cosine terms. These can be rewritten as a sine term with an offset. To see this look at sine and the angle x an offset of k we get sin(x+k), this becomes sin(x)cos(k) + cos(x)sin(k) so by picking k appropriately we get constants cos(k) and sin(k) to turn the sum of the sine and cosine terms at that frequency into just one oscillation at that frequency but offset.

[@not-so-comfortable1935]

@ 11:36 I THINK in the cosmt it would mpit/l

[@abdullahjhatial2614]

pleas explain n ,and m why its only interger ? what excalty m ,n is ?

[@carultch]

They are multiples of the fundamental frequency. For this introductory example, he's sticking to the discrete Fourier transform, where they are integers. There is a continuous Fourier transform where n isn't necessarily an integer, but it is beyond the scope of this introduction.

[@charlesAcmen]

i am back,i am so back lol,been watched this video for the last few months for many times ,always forget how to calculate,always forget what is the coefficient for each term in the equation.

[@jehanrassdeen7928]

Sir what happened to the summation when we get the value to the coefficients.( At 4.19 min )

[@pratikyadav6036]

What will summation do there when its cosine function is not there, as cos nt got cancelled, it went away with it

[@hazemhidouri7608]

In the example at 7:13 what if we want to calculate the coefficients of f(t)=1 from 0 to 2pi instead?? i have a feeling this would give f(t) = 1 always 😂😂, maybe that's the midpoint thing in the the theorem 😅😅 anyway if anybody could help with my confusions plz let me know in the comment

[@arbaazmir854]

Why can't the Fourier series be applied to non-periodic signals?

[@sroydetroy6404]

why is a0 considered to be the period of sine?

[@carultch]

It isn't. It is more like a constant that depends on the average value of the function being integrated. In an electronics application, this would be called the DC offset.

[@sroydetroy6404]

Sorry for the late response but thank you very much!!!@@carultch

[@hz6612]

Your first video was very nice and so helpful but this one confused me so much and i didnt understand at all ...

[@menozmenoz]

i know it's too late , but it would be good if you could normalize the audio of your videos, you go from shouting to whispering. I am using an extension to compress the audio to mitigate the problem. great videos by the way, thanks!

[@IntisarJabir-zj3zl]

Teachers tend to use that method to attract attention on matters that truly matter, maybe reduce your volume idk 😅

[@secularbanda1808]

Sir we are waiting for fourier transform please make that video....🙏🏻❤

[@djab20001]

There is a mistake in the general case a_0 is equal to 1/2L times the integral not 1/L.

[@charlesAcmen]

I am back again,lol,so every time i encounter integral of trigonometric function with power raised to some n variable ,i realize this video but find out that there is no power raising lol,and i proceed to downgrade by using decreasing power expanding degree formula for sin and cos.Alright,thank you again

[@mirziyopardaboyev7755]

Math is so beautiful

[@astroandriodrox2356]

Anyone else learn this by the sampling vector then the complex Fourier series first ?

[@hansisbrucker813]

How did Fourier discover all this 😳

[@abhijeetgore310]

Hey Can u please cover mensuration 3d😶

[@Fidel-tk5rq]

Thank you for sharing these first class lectures .Please advise on the convergence of the Fourier series of a function f(t) =t^2 ( t squared) if 0