Fourier Series: Complex Version! Part 1
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- čas přidán 4. 07. 2024
- There is another version of Fourier Series: the complex form! In part 1, we look at the general form of the complex Fourier Series and then find an equation to calculate the coefficients of this version.
NOTE: @ about 3:00, the cosine(nx) formula has an extra i on the bottom of the fraction. it should be: cos(nx) = (e^(inx) + e^(-inx))/2
Questions about this or other math topics?? Leave a comment and let's tackle it together!
Derivation of Euler's Formula:
• Power series and Taylo...
Links to the sine and cosine Fourier Series:
Part 1: • Fourier Series!! Part 1
Part 2: • Fourier series! Part 2
Part 3: • Explore Fourier Series...
Like these videos? Please support my work by contributing to patreon: / jenfoxbot
Oh my god! I have been spending a full day trying to clarify so many things about this. Thank you so much for this video! Was exactly what I was looking for.
Yayy so happy to hear it was helpful !!
Just love everything about you plus the content
Easy to follow, very useful.
Glad to hear!
Very nicely explained!
Thank you! Glad you found it useful :)
I was lacking in this topic but today all the doubts were clarified. I wish my institution professors were this good
thank you! glad it was helpful
thanks for the lecture
Most welcome!
Beautiful video and beautiful person! very helpful!
Good video,subscribed
Awesome, thank you! 😄
You are so funny. I like this way of teaching. Break a leg!
lol thank you!! glad you enjoyed it 😄
Is there i in denominator of cos?
very good i like study it.
Thank you !
You are great , Thnx from Egypt
Thank you! Glad it's helpful!
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@@abdallahissa2821 hi! I'm super busy but if you have topic requests or Qs, feel free to leave em here!
@@JenFoxBot wanna study math and start in scientific research , but I am really confused , I LOVE math ,but I don’t know how to start , Can u help me :)
@@abdallahissa2821 what are you interested in learning/doing? The more specific you can be the better, or at least a field. For example, do you wanna study stars or the oceans or ostriches or trees or disease or people or brains..? Math is applicable to almost everything, so any math skills you learn will be helpful
Question I was watching a video from blackpenredpen, dealing with this problem, in the video , he uses eulers identities, with just a 2 in the denominator for sine , could you please clarify whether this is correct or not. Thank you.
Sine(ix) should have a factor of 2i in the base, but cosine(ix) should only be 2 in the denominator (my cosine formula has an error but sine is correct).
Brilliant video - thanks for making and posting. I'm new to this so I don't understand how the bounds of integration changed from -ve infinity and +ve inf. to -pi tp pi once you multiplied the integral by the complex conjugate. Sorry to be thick!
Thanks so much!! Glad you found it helpful :)
I think you mean the summation sign range? The f(x) = [summation sign stuff...] is the representation of the (infinite) function (the details of which we can find using the fourier series approach).
The integral bounds are -pi to +pi b/c we have a repeating function, so as long as we are integrating over one full period, we know what the rest of the function looks like, from neg. infinity to pos. infinity! Note that the interval may change if you have a diff. equation, which is why drawing a picture of the function is super helpful. Hope that helps! LMK if you have any follow-up Qs.
@@JenFoxBot Hi Jen, thank you for that, it makes perfect sense now!
thanks mom !
nice
Thanks for making these lectures they are great. I wonder why is it that we can assume, if for example , C5 is larger than C8 and with C8 being very small in comparison, we could ignore Cn larger than C8? Is it not possible that C103 is larger than C5?
the coefficients correspond to the amplitude of that term (i.e., how much a particular periodic function contributes to the overall function we're representnig). the example i gave is just one possibility where the coefficients decrease. but, for example, if we're looking at a sound wave, we could expect that to be the case b/c the amplitudes of the higher frequency terms (e.g. n = 108) are much less than the earlier terms (e.g. n=8). hope that helps!
Ok so that was the average value of the function what if we find the solution of general equation with - infinity to + infinity?
Does it converge or diverge? With complex form of exp(ix)?
+1 to Haseeb's comment! After figuring out if it converges or not, you'll want to figure out if the periodic function is odd or even (one of those will cancel out over that interval). Then you do the same thing - break the interval into smaller pieces where you can evaluate the function.
Hi beautiful!! You are good in what you are doing!! Love you!!!
Hi , when it's better to use one form over the other ?
Both the complex form.and the sine-cosine form give you the same result, just in diff terms (you can get the sine-cosine form from the exponential form). Sometimes the complex form is easier and faster, but it depends on the problem. Hope that helps!
@@JenFoxBot Another question please : Can I say that fourier series is for periodic functions and fourier is for aperiodic functions ?
@@mnada72 oh you mean the diff between fourier series and fourier transforms? Yes, you are correct! Fourier series are for periodic (repeating) functions. Fourier transforms are for non-repeating functions.
@@JenFoxBot Thanks ...
Good luck to foxbot industries
Thank you !!
I think you made a mistake in cosine equation of Eurler's formula take a look in your vedio an check it
Please check video desc. before pointing out errors.
Sorry that's my fault l had an exam and l was very hurry to see some videos so l didn't notice it
benickatak
You are very beautiful ❤️
2:51 You got the cos(nx) formula wrong, if cos(nx) is meant to be a real function. This shines out of the board as a matter of fact, hurting the viewer's eyes.
lol it always amuses me how much folks love to flex their ego. Not only is your comment rude, but there is already a note addressing it in the description. please practice kindness when you choose to point these things out. it will help you feel better.