Intro to Fourier series and how to calculate them

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This is a basic introduction to Fourier series and how to calculate them. An example is presented that illustrates the computations involved. Such ideas are seen in university mathematics.

[@Mughrabi97]

You just saved my semester sir

[@ura239]

I've done a lot of work on Fourier analysis, and it still remains one of my favorite areas in mathematics. The Fourier transform of the quadratic exponential..i.e. (e^(x^2)) is fascinating .....thank you for posting. ...

[@RIPpudrow]

You have no idea how much this helped. I've been in PDE's for a month now and my teacher hasn't been able to explain this so simply!!

[@A1Zealot]

Thanks so much! I'm in intermediate engineering analysis at UF and you've already saved me in the first week when other resources didn't seem very helpful.

[@jaysbay11]

u've just simplified this for me. i've got an exam in two weeks and i'm more confident of aceing it now.thanks.

[@thekhmer2507]

Dr. Tisdell, thank you very much for sharing your knowledge with us. I've been watching a lot of your lectures on youtube. I can't afford for school right now, but with your generosity i'm now in school... Again thanks.

[@nvrfollowb5]

You make a great online math tutorial. One of the best I have seen. Thank You! Keep the PDE stuff coming!

[@drdread]

You, my good sir, are amazing. Your effort is much appreciated. Knowledge is power!

[@adastra123]

Thanks , you have a very elegant way of explaining it. Thanks so much for uploading this. People like you make the internet a toy of the gods and worthwhile. Thanks again so much.

[@AngelloMaggio]

You don't understand how much this helps. I'm a computer science major, who recently decided to double major with physics as well, so I jumped in and took two courses, Intro to physics and PHY 307 which is advanced mathematics for physicists, and it kicked my ass. Thanks yo this video I'll catch up hopefully soon, thank you very much!

[@BentHestad]

A magnificent, little lecture! Very helpful! Thank you, Sir!

[@arienette820]

This video is the only reason I got any of my homework done. Thank you so much!

[@shaheenhearts]

i know you here this a lot!!! but seriously THANK YOU :) really nice of you to go out of your way to help people

[@abekmuratov]

The way u teach is easy to understand and ur voice nice to listen! Thanks from Kazakhstan! Keep it up!

[@megamarch01]

Thank you so much, Dr. Tisdell, for sharing your expertise here in youtube. :)

[@caseysmith9443]

How did you use Maple to come up with that plot? I have a project right now and have the F.S. of our function but can only get the plot to show one "cycle" of the periodic function.

[@soldirix2666]

Thank you for this ^^. That even/odd method is very interesting ^^. You learn something new every day.

[@SheepCountings]

Why is there a little window left in the bottom of the screen with a man imparting a class?

[@amandadube156]

To distract us from the otherwise brilliantly demonstrated problem, I guess... :-/

[@DrChrisTisdell]

That's me, it doesn't match up with the main picture. if it really bothers you then try covering me up with a post-it note, or just your thumb.

[@CrushOfSiel]

Dr Chris Tisdell lol

[@JAKETHESNAKKE]

was scrolling in the comments for an explanation to that little dude in the corner

[@davidfairchild1991]

Using this for my Mechanical Vibrations class... Very thorough and informative. Thank you.

[@DrChrisTisdell]

Yes, that is a great suggestion. I do have some videos on Fourier Transform and convolution, but I also plan to do it for Laplace transforms.

[@74dorset]

Absolutely excellent video. Thank you so much for making this.

[@voidsonvoid]

You are amazing. I was about to give up on this if it had not been for this fantastic video. Thank you.

[@mangoqualifier5854]

can someone explain the bit at 7:40 where he's talking about doubling the integral. Why did we write 2 in the numerator outside and how does doubling the integral -pi to pi make it go from 0 to pi?

[@texxmexxtexx]

Thank you for this great, and easy to understand lesson. It is much appreciated.

[@rkjab]

Hello! I have a question. Does all cosine and sine functions of period 2pi are orthogonal to each other, even if we take L as 2L? or in other words take frequency 0.5?

[@DrChrisTisdell]

@golnar 2k-1 will always be an odd number and it appears as we are only summing over the odd values. Hope this helps.

[@Rmpf22]

@DrChrisTisdell How did the 2/pi become 2/(n*pi)? You just integrated the sin (nt), did you? Thank you

[@asianflex786]

at the start on his formula sheet you can see that fourier series is a function with general period 2L where L is to be found. Now equate 2L to the period in the example which is 2*pi. and divide both sides by 2 to get L=pi. If your struggling to find the period look on the graph where it starts to repeat from -pi to pi which is a span of 2pi.

[@DrChrisTisdell]

Great to see that you have turned "an enemy" into "a friend". J. Fourier would be proud! Hope you also take a look at my new ebook. The free download link is in the description.

[@nadiyayasmeen3928]

But it says 404

[@DrChrisTisdell]

And it's very nice of you to post your feedback - thanks!

[@PHILANTHROPIST1988]

thank u very much sir , u have saved my life your lectures are awesome and easy to follow

[@DrChrisTisdell]

Thanks for your feedback. If you found this video helpful then you also might like my new ebook. It has many more examples and is free to download - the link is in the description.

[@youwuyou]

Hi doctor chris， is the Fourier series elongated twice by period？

[@josepaul2000]

Out of curiosity, what is the small video running in the bottom right? Is that the class for this topic?

[@DrChrisTisdell]

Hi - what do you get if you integrate sin (nt) with respect to t?

[@vojtechdybala5525]

Hello Chris, need to say your lectures on FS are great = simple and clear. Didn't you consider to look at this "problems" from a different point of view? I mean something like reconstruction of a time domain signal from inputs given by e.g. PSD in a frequency domain.

[@PenguinRecordings]

I know people don't say this a lot on education videos, but I think I am going to have to break the replay button for this one...

[@DrChrisTisdell]

My pleasure. If you found this helpful then you also might like my new ebook. It has many more examples and is free to download - the link is in the description.

[@DrChrisTisdell]

Hi - thanks for the comments. In the theory of Fourier series, the value of L is usually HALF the period of f. In this example we have f with period 2\pi, so L=\pi.

[@lminors]

@DrChrisTisdell In this answer, why does a0 go to a half, even though it is odd. I got the wrong solution and I can't see why, is there a worked answer?

[@DrChrisTisdell]

Thanks for commenting and good luck with Fourier series.

[@NevermindVzla]

Alright alright I have an exam in an hour and a half and I must this really helped a lot but I'm still confused with that thing you did at the end with the cos... how did you turn that into (-1)^n ? will it always be like that ? is there a different transformation for sin ? please help

[@SantaMain]

I have a question! If we take a harmonic wave added to another harmonic wave, and then want's to calculate with them. Lets say that we have f(x)=3sin(3*pi*x)+4sin(4*pi*x), this will result in f(x)={6,8381 0

[@sonnynsz]

Thank you for uploading this video, I sincerely appreciate it . It helps me alot .

[@DrChrisTisdell]

My pleasure. Hope the free ebook is also of some help to you. The link is in the description.

[@DrChrisTisdell]

Hi, what do you mean but "upperlimit" and "lowerlimit"?

[@andrewreid82ar]

I know it may appear as basic stuff. I've been going through the Fourier series but keep getting stuck, I cant work out how to draw the graph. Do you have a video that goes in to this. Cheers

[@sarahsshadow]

Thanks, this was so helpful! Any chance you could do one on complex fourier series? :)

[@HeshamSalehVEVO]

Thanks a lot for this video Dr. Tisdell!

[@DrChrisTisdell]

@lugiachan Because n = 2k-1 is always an odd number (whenever k is an integer) and we are only interested in summing over the odd values of n.

[@commelions]

hi im new to this integration stuff, i got a problem with the Bn part, when the integration is done on the 3 line of the bn coefficient you have no t squared left when you move the N outside the brackets. why ?

[@DrChrisTisdell]

My pleasure. Glad you found it useful.

[@shyamnarain]

Amazing Explanation Dr. Tisdell . I would like to know if you have a video explaining Complex Fourier Series. Please guide me if you have lecture notes or explanations on complex Fourier series.

[@DrChrisTisdell]

@ELT626SSN Some texts prefer to have a_0/2 in the Fourier series (rather than just "a_0"). In that case there is no "2" in the (integral) definition of a_0.

[@adityamorey9251]

thanks alot sir... this helped in my exams.. respect from india..

[@DrChrisTisdell]

@aandreya Many thanks for your comments!

[@EvageliAiga]

thanks Dr Chris...I like Fourier series now coz i understand but it was my enemy in class six weeks ago..thanks alot..exams next week...I will watch more and more of your lectures..thanks again...

[@dakanke]

can someone please explain what happened at the last party where he made the cos become (-1)^n?

[@DrEnginerd1]

what class do you typically learn fourier series in? differential equations or an engineering class?

[@flyingrocketman5668]

Your videos are very helpful, and your voice is very nice to listen to. :) Thanks!

[@DrChrisTisdell]

Hi, if we are only interested in odd values of n, then 2k-1 is always odd (for k=1,2,3,4,..) so we can replace n with 2k-1 and we sum k=1,2,3,4 etc.

[@SantaMain]

@SantaMain My problem is that, You have worked with square waves right? and this one is a sine wave.. which makes in more,. non square :D And then i just wonder if it's the same. Thanks :D

[@DrChrisTisdell]

Yes, Sf(t) is the Fourier series of f(t). If f(t) = t then which interval is it defined on?

[@DrChrisTisdell]

Many thanks for the feedback.

[@benjamincordes207]

Very helpful thank you very much. Good explanation.

[@jasonsweet228]

can you describe 2 separate square waves mixed into 1 signal that are offset by 50% from each other so + of one wave and - from another wave hit at the same time?

[@DrChrisTisdell]

@golnar Yes, if you want to "simplify" the sum. It would also be OK to leave it without changing to 2k-1 (or 2k if you are summing over the even terms). It depends on your preference.

[@shusha188]

thanks a lot, but can you please explain how do we we rite 2k-1 instead of n, i dont understand it, for exampl eif n=3 then (2*-1) is 5 which is not true

[@DrChrisTisdell]

HI - that's me. It is probably not this particularly class, but I included something like this just to put a "face" to the voice with the aim of humanising the presentation a little. There are some claims that this can lead to better learning outcomes.

[@NevermindVzla]

@DrChrisTisdell I figured it out, thanks ! My exam was postponed for today, any last minute advices Dr ?

[@ghasemmanouchrhti10]

you're a saviour, many thanks

[@Sasotzu]

Thanks a lot, very useful video for a frenchie who wanted to work for the holidays :)

[@akshaydeshpande7926]

I was wondering to the question that you gave us at the end , what solutions did you get for a0 and an. We know that bn= 0

[@DrChrisTisdell]

@csGolddragon No, what I've said is correct. If h(x) = f(x)g(x) with f odd and g even then h is odd (ie, h(x) = -h(-x) for all x). You can prove this (or just confirm it with on wikipedia).

[@HumphreyBriggs]

How come the final answer you are summing up from k=1 to inf? If you look at the initial fourier formula it goes from -inf to inf? Should it not be k=-inf to inf? Is it because during integration we have multiplied by two as it's an even function so the -inf to 0 is taken care of? Thanks

[@aminulmizi6275]

Would someone be able to explain how he was able to change the limits at 7:35? Thank you

[@TheMunkification]

Where did the "n" and the -2 in -2/(n*PI) come from at 08:24 ?

[@DrChrisTisdell]

In most examples it is the function that you begin with. In this video it is f(t) (of course, neglecting points of discontinuity etc).

[@DrChrisTisdell]

My pleasure and hope you find the ebook useful, too. The free download link is in the description.

[@woo216]

thanks these videos are very helpful, can you please do videos on the Fourier transform

[@amandadube156]

How would you find a0 if the function was even? I'm getting caught up on weather or not I need to integrate the left and right sides of the y-axis separately.

[@amandadube156]

Also, can you always limit the range to positive L by multiplying the function by 2, or is this just a property of even functions?

[@viktorgoa]

this helped me finally understand it, many thanks!

[@akshaydeshpande7926]

Thank you sir, I was wondering whether there is a video on Fourier Transform?

[@kakakakaka9999]

Hi Chris, thank you for this tutorial, it was super helpful!! One thing that confused me was the period -why isn't it L=2π?

[@patarthenry]

Thank you for this example with explanation.

[@DrChrisTisdell]

@shinakuma9 Please read the annotation at the start of the video for directions.

[@nigelnelson1735]

Thank you, this was very helpful.

[@jazzymelmel]

thank you! how did the n become 2k-1...?? is that a trig identity? :( so confused

[@hellbark]

what if in the piecewise function, there's and odd function and even function at the same time??

[@safkanderik7217]

Hallo Dr Haveyou a A video about Forier Series that explain how to reach the general Form? Thanks.

[@DrChrisTisdell]

The aim is to formulate an expression for b_n. Depending on what n is, the value of b_n may take on various values. In some examples, if n is even then the value of b_n can be simplified; while if n is odd then the value of b_n can be simplified.

[@sansiddhjain]

Dr. Chris, wouldn't the function given here be non-integrable?

[@Our_Sole_Pusch]

Hello, I have to say that these are the clearest explanations yet of Fourier that I have seen. I have come unstuck at the end problem though. I keep getting the a_n coefficent as (2/(n*pi))*Sin(npi) = 0, but now they all = 0? Thanks

[@DrChrisTisdell]

Well done - you answered your own question.

[@DrChrisTisdell]

Hi - this is a deliberate educational strategy of mine. I have provided hundreds of solutions on KZbin but I am reluctant to do so with the questions in my ebook.. The questions in my ebook are designed to challenge, inspire and even frustrate learners at times. This is all part of a holistic educational process to make you learn. Thanks for the feedback!

[@biloocabba2]

thank you sir ...i study in 1 years master Electrical Engineering, and i hope that ..benefit from your extensive experience bilal

[@DrChrisTisdell]

@NevermindVzla Yes, it will always be like that (can you see why?). There is also one for sin, but I'll leave it to you to determine it. Good luck with your exam!

[@Mjorh]

Thx Doc ! Magnificent ! plz make more examples...

[@DrChrisTisdell]

@lminors Correct - the function isn't even (I didn't claim that it was). Think of shifting the curve down 1/2 a unit to produce an odd function and calculate the FS for that. Then simply add 1/2 to your answer. Over and out.

[@lifepari8486]

Please Mr. can you say that how we know that a function is odd or even ? can you help me please ?

[@DrChrisTisdell]

My pleasure and good luck with Fourier series. Hope the free ebook is also of some use.