Fourier Series: Finding a Fourier Series Representation of a Function
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- Опубликовано: 2 дек 2024
- Fourier Series: Finding a Fourier Series Representation of a Function
In this video, I demonstrate how to find the Fourier Series representation of a simple piecewise function with a period of 2. The process is lengthy but essential to understand for anyone studying Fourier analysis and its applications. Although I do not provide a proof for the coefficients' formulas, I use the theoretical background from earlier videos (check out the playlist for more). By the end of this video, you'll be able to break down a function into its Fourier series components and gain insight into the representation of periodic functions.
If you enjoy my videos and find them helpful, please subscribe, like, comment, and share with your friends, teachers, or parents! Your support helps the channel grow, and I truly appreciate it!
What You Will Learn:
How to find the Fourier coefficients for a piecewise function.
How to set up and evaluate the integrals for coefficients.
Understanding the sine and cosine series that make up a Fourier series.
Applying the formulas for a_n and b_n and a_0 to represent a function.
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Test in 2 hours. 1) Open the channel. 2) Watch the video. 3) Done in 20 minutes. 4) Practice. 5) Ace the test. Thanks Patrick!
i hope the test went well!
patrickJMT It did! :-)
You must have a job now bro. :/
lol
No. 5, barely pass/fail the test
I've struggled with this for 6 months and you've made it clear in 20 minutes. I don't have words to thank you enough.
what I find neater, is not the function, but the fact you have helped hundreds and thousands of people with maths. I reckon you'd feel pretty good about that Patrick.. Thanks for the video it's really appreciated!
I saw your video about the revenue cut and being a Patron. I then remembered this particular video. If it hadn't been for this video I don't know how Continuous and Discrete Signal Analysis test would have gone. So thank you Patrick for teaching me how to compute the Fourier Series Representation of a Function. I am heading over to Patreon Now as all of your math videos have helped me more in life than my $10 netflix account or my $10 spotify account. Good luck!
awesome :) thanks brother!
Would you be able to do a video for us on the points of convergence for the Fourier series we came up with in this video. Thanks for your great teaching :)
Patrick is da real MVP
I love how this guys makes topic the easiest it can be unlike all these university lecturers who just assumes we already know everything.
Thank you so much, the step by step progression that you use makes everything so incredibly clear when previously it looked like a whole bunch of random equations thrown together with no continuity.
This topic alone was the reason why I dropped my Quantum Mechanics class. This was never taught to me and for the life of me I could not understand it. The last 20 minutes was perhaps the best spent time in my life thus far.
Missed a few days of class from being sick, so I was completely lost when I came back and everyone was talking about Fourier series and nothing else I looked at helped me understand it whatsoever
You're a total lifesaver, man
2L = period. (standard formula)
And since period = 2.
2L = 2.
and L =1.
Thank you
thanks man
You read my mind
Thank you!
Darren Ng you’re a saint, gentleman, and a scholar
how's this bro, been saving me since 9th grade and now I'm about to be in my 4th year of engineering . Absolutley insane. Him and "organic chem tutor" are the absolute legends of the core science based classes.
Seriously you basically taught me the entire Calc Series and Linear 1 and now this is saving me in Linear 2. THANK YOU. So blessed to have such a clear way of learning this material available to me through your videos. So helpful, you have no idea how many of my fellow engineering friends have used these videos to learn!
+Braeden Small
Remember to donate to his Patreon when you make it big :)
My end of semester tomorrow... Im clutching on your tutorials.. Thanks big..
How was the exam
Please do another harder one! Also thank you for your videos, I cannot describe how valuable of a resource they have been for my classes.
Thank you so much, Patrick! You are a life saver! I didn't understand Fourier Series at all until watching your video, now I think I can get them down in time for my final!
Patrick you are the best !!!
you explain things smoothly and as if you are reading what's on our minds.
Thanks in a million.
One of the only decent Fourier Series videos out there.
i dont even know who my math prof is or when the section hours are thanks to you. really convenient and time efficient videos. that was the last term with math for me but i suppose im still gonna linger here for a while.
These videos are the only reason I survived my university math classes, great job as always. :)
You are the best ! So much better than any faculty at my university !
+Inzamam Ul Islam
LOL, your faculty must suck ASS!
...just like mine :(
Looooong time fan... Slowly learning to spreche Mathematics... Praise the Gods for that and you, Patrick. You are a serious reason why Mathematics is accessible to people of all backgrounds and that is PROGRESSIVE. Om Shanti.
This channel deserves several million subscribers :)
This is not simple, but it's very satisfying when I get it right. Good video !
how do i unlearn the complicated way my teacher taught me? :-( :-(
wish me luck. taking the board exams for electronics engineering. been using this for review. thanks for everything.
+Lawrrence Lozano Good luck!
GO ECE!
patrickJMT just so you know, i'm already a licensed electronics engineer! thanks again! :D
anu review center mo pre? haha
Christian Rey Bautista RF dito sa cebu. :)
Awesome video. Been using your material to help me for four years running. Bout to start graduate school for electrical engineering (undergrad is biomedical). It would be epic if you did a video on wavelets!
Thank you so much! You have helped me understand the material in so many classes that I've taken. You help a lot of people and it is very appreciated.
Patrick for President! #YOUDECIDE2016 #PATRICK #MATHCRATPARTY
for some reason this is finally starting to click after watching this video, thank you!
have to say you saved my session. Good work! I wish my teacher would explain as good as you.
I learnt this topic in college 5 years ago from this channel and now I had to study for an exam. I didn't remember the channel's name and had to search using so many different keywords but at last I found it I feel so happy 😭
I also want to thank you for this because you helped me clear my math exams 5 years ago🥺
I know this is late to thank but better late than never. right?🙏
glad i could eventually help you out :)
More confident for my finals now :)
+Javed Baball he made it look so easy
+Javed Baball Sup guyss :). Fancy seeing you guys here
- Chike (Worldboss)
Thank you. This is one of the clearest examples available on Fourier Series.
Thank you Pat. It's the hardest series of equations I had done so far
Really thank you man .. you helped me a lot with Math
One thing I noticed , when you calculate a0 there is a mistake in the integration
you should end up with x/2 not 1/2
But really nice job
Keep up the good work
Thank you , i was looking in the comments for answers :)
Very helpful, thank you! Have my Differential Equations exam tomorrow :)
passed calc 1,2,3 all because of u :)
What really made shit a brick was when I was doing circuit analysis in one of my physics classes and found out that low/high/band pass filters work off the Fourier series! It's not just a mathematical tool (which I could be mistaken but I think that's all Fourier thought it was), but an actual correct physical representation of a lot of cool stuff!
just want to say thanks man. videos helped me alot before finals. BOOM!
the way you teach is so helpful.
appreciate a lot...
Oh my word, this helped so much! Thank you!
Definitely enjoying this series. I think some of it is going over my head, but it makes me think, and it's good to have the challenge of trying to digest something new. It means when I do come to it properly in the course of my studies or later on, it'll be partially digested already :)
keep going patrick
your style in vedios is perfectly perfect
I love how you make hard stuff like this easy to understand ❤️
You've made really clear explanations. This is truly extremely helpful. Thank you so much.
I have been searching this for hours .It's awesome ^_^
nice math well done soon people will start copping your work
This helped me to understand the basics. Many thanks.
Could you make another video about Fourier series. Ex: odd and even, more exercises. Because you are great on that.
Thank you for your amazing job.
Patrick you just made our lives so easy :-)
Yes videos form 2006 are helping me
So, I can do Fourier series because of you. Thanks!
You sir are heaven sent. Thank You
Thanks a lot. Saved my semester
I'm a 10th grader trying to understand Fourier Series, this clears the computations up a lot, thanks!
WOW. Great video. Thanks for sharing for all to learn!!
thank's PATRICK you are a life saver
Fantastic stuff Patrick!
I use your videos all the time, you're without a doubt the best.
When do you think you can post some videos on Wronskian ?
Thanks Again
you are a hero patrick!
Thanks so much Patrick, this was an awesome explanation.
you teach better than my professor
no, not any time soon. other stuff i will do first: more diff eq, more linear algebra, statistics.
Great tutorial by the way.
From 10:45 onward, I think A0 = 1/2x because it is an integral with respect to x
+Richard Opoku Actually the x is then substituted with 1 and 0 from the definite integral, so it become 1/2(1-0) = 1/2
I actually thought the same thing then realised that I was wrong
Thanks !
Plz do more of fourier series.
What a great video, your students are lucky
thank you so much Patrick you are amazing.
At 17:51, It is actually 2n -1 not 2n+1
sphesihle ngcobo it’s not, because he corrected himself and let n start at 0
Thank you, Patrick! Wish you could be my professor at school!
i for one would love a more complicated example :) thanks for the help!
This is great patrick. Thanks alot
Been watching since 2011 and you helped me all the way from precal to PDE's now
شرح اكثر من رائع ...شكرا اتمنى تنزل بعد اكثر بما يخص التحليلات الهندسية وفقك الله
please do another more complex example.
Thanks Patric. You are amazing
+Omar Alnajjar just helping the best i can!
Hey, that 20mins 32 seconds presentation made me realize one thing. You're way better than my smart-assed math instructor. But I have this problem on fourier I just couldn't get. Maybe you could help me out? f(x) = x^2-x+3 from -2 to 2. Please... I'm really having a hard time with that. Ugh! And I bet you're the only person who can help me.
mmaybe complete the square and split the f(x) into 2 functions? like f1(x)= = completed square and f2(x)= remainder of square?
Thanks for the clip dude, You are the best !!!!
Thank you patrickjmt!
Excellent I was getting mad Have my calculus test tomorrow
great explanation💯
Really great video, thank you so much, it's so great
great presentation from you my friend. thank you
thanks bro very helpful good work keep it up
I knew it was easy but never thought this much easy. Thank you , especially for the graphical representation
Get your punkass out of here, you are so full of yourself that you probably can't even see straight. I have friends who are there PhDs in physics and they tell me how much they hated fourier series. Because it can very tricky
great job sir! it was very interesting
patrick you are legend
Actually, I think doing that is completely valid, from what I remember from my Engineering Analysis 2 class.
This is a great video! What if the intervals for f(x) are 0
I guess they use Fourier Series to predict the tides, but I would love to see the actual function used, and how it incorporates the moon, the sea floor topology, ..., and the sun's influence here in the Gulf of Mexico.
O wise one, i know this might seem a little overkill for a non-audio enthusiast (an assumption), I'd recommend a condenser microphone with some decent audio interface box then you'd never need another mic + you'll have excellent audio. Ben
REALLY REALLY USEFUL
Many Thanks !!!
I have 15 years temperature data. I want to remove seasonality variation from the time series data, so how can I get the constant term ao, the amplitude and the phase change by using these given temperature data? thank you
So for the fourier series representation part, do we just add those dots at the average of our graphy. So for example for the function f(x)=cos(x/2) would i just put the dots at y=0.5 and x = 2 pie??
Good work bro
you are awesome JMT
nice review video on fourier series. My applied linear algebra course covers this topic when dealing with the concept of inner product.
you saved me again, thanks!
could you do another video to solve this in complex form?
thank you for posting this video
Thanks a lot patric bro.
I wish you were my computational physics professor
omg thank you so much for.
This stuff were killing me, but now it's all clear :D