@@NotYourAverageNothing since a_0 is a constant perhaps he defined his a_0 as your a_0/2 anyway if u use a_0 or a_0/2 for the fourirer serie, you have to use the same constant for the parseval solution and everything is gonna be fine :3
You are the best when it comes to Integration and derivatives. I wish you were my teacher irrespective of your pronunciation!!! Who else wants BlackpenRedpen to be their Mathematics Class teacher?
Anyone going into signal processing, a branch of Electrical Engineering, make sure to understand this problem and its family. Fourier is used heavily in signal processing and will be a major part of your associated courses. Don't ask me for help, though. I understand the concepts, but this was the hardest of my engineering courses.
Cody Lynn same here...problem is we didn't understand the purpose of subject....for me most difficult topic was z-transform. ..I still don't know where we actually use in real life
The thing is that things that are hard in the time domain become easy in the frequency domain and vice versa. Filtering is implemented in the time domain is implemented as convolution of the time domain signal with the filter impulse response which can be computationally intensive. In the frequency domain it is just pointwise multiplication. Therefore you can implement filtering in the frequency domain as long as you make sure that your implementation avoids aliasing in either domain.@@jaikumar848
i am searching for more than 1 hour and finally got your video . you have explaibed this formula properly .no one on youtube have explained like you , i have watched 15 video on parsevel theoram and was not getting it . finally got it from your video
This is the last thing I've seen on a blackboard before starting to study math by myself, and I had to know by hearth because I did not got the theory. And you made it accessible to me. Thanks BPRP, so fulfilling, thanks!
That reminds me a French joke I made up in high school: Q: Que dit le thé à Parseval? A: Je suis un thé Graal To which my math teacher added: A: Je suis toujours là, je suis un thé Graal pas reparti (= par parties)
what might actually be an intuitive and more straight forward rationale for the intuition of parseval's identity is the fact that. if you calculate the energy of the original signal, that would equal the sum of energies of all the harmonic components for that signal. Thats all parseval's identity says.
The sum of 1/n^3 will lead to you having to integrate stuff like x^3/2cos(nx) and x^3/2sin(nx) which will not lead to nice answers. You can get the sum in terms of integrals which is not that nice.
Today is my birthday And this video is a great birthday gift But I want a gift from blackpenredpen...... Please explain Riemann zeta function... Please 🙇🙇🙇🙇🙆🙆
This is gold man! Btw just a small mistake in the Fourier series... it's ao over 2, not just a0. Anyways it's the ideas behind this proof that make it 100% worth it
I guess is not possible to use Parseval to obtain the summation of 1/n^3. I suppose that we should use f(x)=x^(3/2) but doing so when we integrate by parts to obtain an and bn we'll never have a 0 in the D column. This happens for integer powers of x only. The same should be true for all the odd powers summation of 1/n.
Hey blackpenredpen, I have a challenge for you. Can you find the approximation of log2(1000) without using a calculator? Many people forget that logarithms were calculated without a calculator when they were first discovered, and many people don't actually understand how they work. I know how to do it (it's tedious), but I think it would be nice to show the audience why it works. Have a great day :)
So you did 1/pi to have the final form without pi in as term. But why not 2pi? Usually this theorem is placed as power so it makes sense to divide over the period
For the third term, I would convert to a double sum first, and then switch the order of summation and integration (assuming everything is nice). I'm not sure what bprp is doing here.
Hello thank you for your video (I'm French so sorry for my English) Can some people tells me why we can also say that f(x) = a0/2 + sum and not with just a0 ? And why have you not show in your video at 5:05 that your sum was an uniform convergent sum (I don't know if we say that in English) for exchange the integral symbol with the sum symbol ? Thanks you
I am a bit late too, but it's in the definition that he gives originally In the beginning of the video, he sets f(x) = a_0 + ... Now, usually not a_0, but a_0/2 is chosen for that purpose, and if you happen to workout the whole sequence he does in the video you get a_0^2/4. Which will then become a_0^2/2 after multiplication by the 2*pi term and dividing by pi.
Completely lost in the following . . . 8:00 onwards . . . How do you prove that ∫f(x)dx . ∫g(y)dy = ∫∫f(x)g(y)dydx ? 8:40 onwards . . . How does a product of two summations become a double summation?
Ur videos are great and I hv learnt so many things from ur channel But, no offence, it would be perfect if the pronunciation is improved Hope ur videos can become better and better Keep it up!! Support
blackpenredpen Cuz English isn’t my mother language as well, but I can distinguish good/ not that good pronunciation. I won’t give u suggestion as I don’t hv this qualification to tell the corr pronunciation But trust me, ur math content is amazing Maybe mimic some native speaker I think lol Non offence, really
If you already know that cos(nx) and cos(mx) are ortogonal if m and n are different, this is easy. If not, yes, integrate by part twice. It is also in any regular table of integrals. One of the many things in maths that you do by hand once in your life and that's it.
U Fourier, I Parseval!
Yay yay yay yay
blackpenredpen why is it a_0 instead of a_0 / 2?
@@NotYourAverageNothing Saw that as well, there might be a mistake somewhere
@blackpenredpen could you pls do the Fourier-series of the function (sin(x))² . Thank you😊
@@NotYourAverageNothing since a_0 is a constant perhaps he defined his a_0 as your a_0/2 anyway if u use a_0 or a_0/2 for the fourirer serie, you have to use the same constant for the parseval solution and everything is gonna be fine :3
You are the best when it comes to Integration and derivatives. I wish you were my teacher irrespective of your pronunciation!!!
Who else wants BlackpenRedpen to be their Mathematics Class teacher?
I'm sure I'd have got an A with BPRP as teacher. And enjoyed my class.
I was angry at maths, and this video made me Furier.
JAJAJA buena hombre
Kkkkkk
Anyone going into signal processing, a branch of Electrical Engineering, make sure to understand this problem and its family. Fourier is used heavily in signal processing and will be a major part of your associated courses. Don't ask me for help, though. I understand the concepts, but this was the hardest of my engineering courses.
Cody Lynn same here...problem is we didn't understand the purpose of subject....for me most difficult topic was z-transform. ..I still don't know where we actually use in real life
@@jaikumar848 bro do you know now why we use z transform
The thing is that things that are hard in the time domain become easy in the frequency domain and vice versa. Filtering is implemented in the time domain is implemented as convolution of the time domain signal with the filter impulse response which can be computationally intensive. In the frequency domain it is just pointwise multiplication. Therefore you can implement filtering in the frequency domain as long as you make sure that your implementation avoids aliasing in either domain.@@jaikumar848
@@depressedguy9467 i do but i wont tell you
@@theodoremercutio1600 because you dont know
As a physicist I love this stuff and its relation to wave energy. Thanks BPRP.
I love when complex problems have such clean results!
The best of the best
Blackpenredpen YAY
This has been the best explanation of Parseval's even after looking through 20+ vids on engineering channels. Thank you!
The treatment is somewhat different from the situation where you have a complex time domain signal with perhaps infinite duration.
I wish u were my calc teacher. We need more people like u in this world.
I’m taking ap calc ab next year in my junior year, and i love you for lighting a fire for me in this amazing stuff
i am searching for more than 1 hour and finally got your video . you have explaibed this formula properly .no one on youtube have explained like you , i have watched 15 video on parsevel theoram and was not getting it . finally got it from your video
6:47 mathematical nihilism: everybody is zero
never enjoyed maths that much ! thank you man
Ashmophobie my pleasure
This is the last thing I've seen on a blackboard before starting to study math by myself, and I had to know by hearth because I did not got the theory. And you made it accessible to me. Thanks BPRP, so fulfilling, thanks!
I dont Unterstand one single Step but i Love how someone Talks about Math with Deep Knowledge
I'll never study this stuff, and still I'm here watching this guy fascinated
Awesome stuff! Got an exam in Fourier Analysis coming up in two weeks, this was a great explanation!
This has to be one of my new favorite theorems.
That reminds me a French joke I made up in high school:
Q: Que dit le thé à Parseval?
A: Je suis un thé Graal
To which my math teacher added:
A: Je suis toujours là, je suis un thé Graal pas reparti (= par parties)
Dr Peyam
Oh! I totally understand it!
Oh Doc! I didn't, I don't even know a Word in french...
Thorough explanation!
Wow that was amazing I totally understood all you said
I love math once again thanks to you
what might actually be an intuitive and more straight forward rationale for the intuition of parseval's identity is the fact that. if you calculate the energy of the original signal, that would equal the sum of energies of all the harmonic components for that signal. Thats all parseval's identity says.
You Mr you have talent of teaching
no, when u integrate x^3/2(f(x)) by integration by parts, u cannot get 0 by rapidly differentiating x^3/2
Also, cheater way: there is no closed form for Aperys constant so that answer isn't doable by traditional techniques :)
pen(black+red)
¿що ти думал?
It should’ve been (black +red)pen
Like matrices
@@tahaabujrad7806 but that assumes that {black, pen, red} are associative under multiplication
Great video! Thanks for the help
Nice timing. Just "learned" this in class on Tuesday.
The basel problem follows nicely from this.
Seth Harwood yes
I love how you say "pi to pi"
The sum of 1/n^3 will lead to you having to integrate stuff like x^3/2cos(nx) and x^3/2sin(nx) which will not lead to nice answers. You can get the sum in terms of integrals which is not that nice.
Wow!!!!! Loved it....
Thank you from Turkey
Very nice. We only used the Parseval's equality back in school, never derived it. :)
I like his energy
Today is my birthday
And this video is a great birthday gift
But I want a gift from blackpenredpen......
Please explain Riemann zeta function...
Please 🙇🙇🙇🙇🙆🙆
see numberphile's video
\\//
@@eshaanrawal1167 already seen
This is gold man! Btw just a small mistake in the Fourier series... it's ao over 2, not just a0. Anyways it's the ideas behind this proof that make it 100% worth it
It can also be a0. The integral to find a0 changes in this case.
Good explanation...love from india 💓💓
Very nice proof.
Good work
I guess is not possible to use Parseval to obtain the summation of 1/n^3. I suppose that we should use f(x)=x^(3/2) but doing so when we integrate by parts to obtain an and bn we'll never have a 0 in the D column. This happens for integer powers of x only. The same should be true for all the odd powers summation of 1/n.
Great video!!
U university, I blackpenredpen
He universities too, though :)
I watch every single video and I haven't even started calc I
Ja, ja, ja, ja
legofanas why?
you're ready for complex variables now
this concept is way past calc 1
Me before using integration by parts:
Is this gonna work
Also me: It will because I don't know what I am gonna do if it doesn't.
Lol. Nice one.
If it doesn't work, you change color, and do it again.
@@Л.С.Мото you mean order. Right?
@@harshitdhimar9647 yes
This is so good❤
Very nice!!!
Thanks!
Thank you.
Thanks a lot! I understand this way better than my maths lecturer (no offence intended towards him).
The sum you have asked for is the Apery's constant, but it doesn't have a closed form :(
My favourite movie: Fast and Fourier
Wonderful
Amazing!
great video thank you
Even times odd is *even*
Vs
Even function times odd function is *odd* function
How odd!
I think it shows the difference between numbers and exponents.
Gordon Chan yea!
When multiplying, exponents are added, so this is like "even plus odd is odd"
Amazing
Wow it is super da
You did consider if series was uniform convergent. What if it's pointwise or just quadratic convergent. I think there should be another way to prove
Thank you.
Does that mean the integral of f(x) dx from -pi to pi = 2pia_0?
Make such videos more it helps me in the competitive exams. Luck from India
Pretty lame comment
Thanks.
Can u do the factorial of i
thank u 👍🏻👍🏻👍🏻🤩🤩
Hey blackpenredpen, I have a challenge for you. Can you find the approximation of log2(1000) without using a calculator? Many people forget that logarithms were calculated without a calculator when they were first discovered, and many people don't actually understand how they work. I know how to do it (it's tedious), but I think it would be nice to show the audience why it works. Have a great day :)
Dacota Sprague u mean slide rule?
@@blackpenredpen Slide rules are neat, but that isn't intuition. I was thinking you try to figure it out (estimate) without any device.
Blackpenredpen did you ever enjoy other subjects when you were In school other than maths and physics? Did you enjoy like History or Chemistry?😀😀
hmm maybe it's time to get one of those clip-on wide lenses for mobile phones and clip it on the laptop's camera to have a bit wider view ^_^
Notification Squad
for thr final answer. i think its [(Ao)^2]/2 not the 2((Ao)^2)
bhai paer kaha hai apke
my signal and system final was a total failure, i dont wanna see anymore fourier :(
I am sorry to hear that : (
Best wish to you
Video on Hilbert spaces when?
But how do we prove it for p=2L ?
Interval [ -L , L ]
So you did 1/pi to have the final form without pi in as term. But why not 2pi? Usually this theorem is placed as power so it makes sense to divide over the period
Is it that the Fourier series formula has been updated?
Because in the formula my lecturer gave us, it is a0/2
Was this on the final?
Л.С. Мото lol actually no.
13:25 don't let the n-word m bother you
I want to move to Los Angeles.
For the third term, I would convert to a double sum first, and then switch the order of summation and integration (assuming everything is nice). I'm not sure what bprp is doing here.
how would this go for a complex f(x)?
BPRP upgraded and got a blue pen
Is this calculus 3?
no. calc 3 is multi variable calc
Hello thank you for your video
(I'm French so sorry for my English)
Can some people tells me why we can also say that f(x) = a0/2 + sum and not with just a0 ?
And why have you not show in your video at 5:05 that your sum was an uniform convergent sum (I don't know if we say that in English) for exchange the integral symbol with the sum symbol ?
Thanks you
well je crois que j'arrive un peu en retard mais regarde cette vidéo
ruclips.net/video/k3byqIaULb8/видео.html
I am a bit late too, but it's in the definition that he gives originally
In the beginning of the video, he sets f(x) = a_0 + ...
Now, usually not a_0, but a_0/2 is chosen for that purpose, and if you happen to workout the whole sequence he does in the video you get a_0^2/4. Which will then become a_0^2/2 after multiplication by the 2*pi term and dividing by pi.
❤❤
GOAT
Great video. Could you do the Fourier Transform and it's Inverse ????????
FOU YAYAYAYAYAYAY
Please. ?
What about( an- bn)(an*bn)..? Is it correct
Using fourier sin to evaluate odd functions?
Completely lost in the following . . .
8:00 onwards . . . How do you prove that ∫f(x)dx . ∫g(y)dy = ∫∫f(x)g(y)dydx ?
8:40 onwards . . . How does a product of two summations become a double summation?
This right here should help math.stackexchange.com/questions/549923/how-the-product-of-two-integrals-is-iterated-integral-int-cdot-int-iint
Peter Chan I also have another example on double summation ruclips.net/video/u1BtAhtCRcw/видео.html
Es el teorema de Fubini
Ur videos are great and I hv learnt so many things from ur channel
But, no offence, it would be perfect if the pronunciation is improved
Hope ur videos can become better and better
Keep it up!! Support
kingki mak
Is there any word that you have in mind that I should pronounce it better. I prob pronounced Parseval really badly lol.
blackpenredpen
Cuz English isn’t my mother language as well, but I can distinguish good/ not that good pronunciation. I won’t give u suggestion as I don’t hv this qualification to tell the corr pronunciation
But trust me, ur math content is amazing
Maybe mimic some native speaker I think lol
Non offence, really
Por que tenes esa bolita siempre en la mano???
Great video. Just hoping that the English version comes out soon.
Trying to be funny?
Clear Sky racist 😒
@@Nxck2440 how does that correspond to race? It's just about fluency you idiot.
If you take f(x)=1/x, Bn part get sick... : ( I don't think it's even possible to square that in the series...
Woooow
No linear algebra, PDE or Complex variables videos?! 😢
Also you used a blue pen here 🙃
Dr. P takes care of those subjects!
Thanks!
Here’s an idea: What is a^2 + a?
Thanks a lot, do you integrate by parts twice to get the integral of cos(nx)*cos(mx)dx ?
If you already know that cos(nx) and cos(mx) are ortogonal if m and n are different, this is easy. If not, yes, integrate by part twice. It is also in any regular table of integrals. One of the many things in maths that you do by hand once in your life and that's it.
Can we always put the summation outside the integral?
no
#Parseval
wtf, parseval is fucking crazy
love u
曹老师在哪间学校教书啊