Im in 3rd year electrical engineering and my class has been shafted by a brand new prof who got his PhD last year, and speaks VERY broken english. Lectures are hopeless, but this series is actually helping a lot! Thanks Sal
Thank you for this video. We just started our Fourier series and transforms chapter in Math 346 and our hw was a single problem! Thank you for showing a clear example!
using the 2pi period to simplify this has actually made it harder to understand.. because i have no idea how to setup the equation for other periods. idk where the periods go.. or where there are supposed to be pi's. Eg my current assignment has a 15V pk-pk, 8000Hz, 50% duty cycle square wave. And I have to calculate the first 3 non zero fourier coefficients. No idea.
I have 15 years temperature data. I want to remove seasonality variation from the time series data, so how can I get the constan term ao, the amplitude and the phase change by using these given temperature data? thank you
cos(0) = 1 so, 1 - 1 = 0 cos(2pi) = 1 so, 1 - 1 = 0 cos(4pi) = 1 so, 1 - 1 = 0 cos(2*n*pi) = 1 so for all even pi, the value of the term will be 0. Vice versa for the odd values, the term will always come out to pi, which is -1 making the inner term -2. So you will have (6/n*pi) where n is always some odd number.
I'm really hopeful that someone can point me toward the video previous to this one, which I am assuming comes between intro to fourier series and this video. I'm having a very difficult time navigating these fourier videos as they have no listed order and seem to jump around from topic to topic. I'm going to look them up by date I guess..
f(t) is some function, that we assume can be written as a series of sin and cos, like: f(t) = a_0 + a_1 cos(t) + b_1 sin(t) + a_2 cos(2t) + b_2 sin(2t) + .... So the first term in f(t) is just some constant a_0. If you wanna find a_0, you simply integrate f(t) over the whole period, like: int_0^2pi f(t) dt = int_0^2pi (a_0 + a_1 cos(t) + b_1 sin(t) + ...) dt = int_0^2pi a_0 dt = 2pi a_0 => a_0 = 1/2pi int_0^2pi f(t) dt all terms like cos(nt) or sin(nt) is zero when you integrate over the full period. So what's left is just you integrating some constant from 0 to 2pi, and that's where the 2pi comes from.
He's doing it that way because you can think of the first b_sub_n*sin(nt) term as b_sub_0*sin(0*t) = 0. It equals zero, which is why he doesn't bother writing it down.
Profs with heavy accents make life horrible for science students. My dad , a very bright man, flunked Calc. for this reason. For todays tuition we deserve better.
Im in 3rd year electrical engineering and my class has been shafted by a brand new prof who got his PhD last year, and speaks VERY broken english. Lectures are hopeless, but this series is actually helping a lot!
Thanks Sal
Ha. This “series”
😢😂🎉😮❤❤😮
@@jacksoncasper8428 😮😮😮
Thank you for this video. We just started our Fourier series and transforms chapter in Math 346 and our hw was a single problem! Thank you for showing a clear example!
2nd year mech eng here who has a final exam tomorrow.. wish the lecturer showed us this instead of his slides
@JayJay Patrick Yes I have brother. Got a first class hons BEng degree and now I'm in a full time job as a design engineer! :)))
Love your videos, thanks for all the detailed explanation. Great job
The expression for a-nought is derived in the preceding video. But the expressions for a-sub-n are not derived, just presented as a formula.
everything has just clicked. thanks so much
Excellent video!
keep the series coming Sal,thanks
Ahhh yesss.... It's all coming together now
not bad. needed help with this. thanks salmon
using the 2pi period to simplify this has actually made it harder to understand.. because i have no idea how to setup the equation for other periods. idk where the periods go.. or where there are supposed to be pi's. Eg my current assignment has a 15V pk-pk, 8000Hz, 50% duty cycle square wave. And I have to calculate the first 3 non zero fourier coefficients. No idea.
from zero to dubaï
why did you use 1/Π on bn and an instead of 1/2Π as used in a0? I'm sorry, this part confused me. 😕
you got the answer??, it confused me too
watch videos 6 and 7 to find the answer
lhiera westmont this is a basic formula to find the cofficents of bn and an .a0 is on dc line so its formula is changed .i just google it
The numerator on an is 2, and the period of this square wave is 2π, so the twos will cancel out and you will have 1/π . Hope that helps 😊
an-2/T 2/2*3.14 1/3.14
8:40 Couldn't you use (-1)^n to represent the even odd nature of cos(npi)?
thats what I did in my work
(-1)^n goes into the complex domain inbetween the integers, but its real part is equal to cos( n pi ). so yeah, for more basic questions it works
n in this case is only integers anyways, so you wouldn't worry about the complex domain.
very good explained
You are just awesome. Life saver.
If im successful in life im donating all my money to khan academy 😭
link to the fourier series playlist?
when calculating b you took its integral from 0 to pi whereas your period at the beginning of the problem was 2pi.
from pi to 2 pi, function is equal to zero, so value of bn for that region is also zero. He did the same in calculating an too.
3:49
Was finally starting to understand until he started getting all fancy here
Fancy where? It's a fine tutorial.
Teşekkürler (Thanks) Khan Academy
I have 15 years temperature data. I want to remove seasonality variation from the time series data, so how can I get the constan term ao, the amplitude and the phase change by using these given temperature data? thank you
can (an) and/or (bn) be negative to allow any degree of phase shift? (For another waveform)
I have a problem getting how when n is even you get zero. When n=2 , cos 2 (Pi) is not 1, it is -1 so it doesnt add up to zero! Please explain?
Thanks
cos(0) = 1 so, 1 - 1 = 0
cos(2pi) = 1 so, 1 - 1 = 0
cos(4pi) = 1 so, 1 - 1 = 0
cos(2*n*pi) = 1 so for all even pi, the value of the term will be 0.
Vice versa for the odd values, the term will always come out to pi, which is -1 making the inner term -2. So you will have (6/n*pi) where n is always some odd number.
Is this function odd, even or neither?
I'm really hopeful that someone can point me toward the video previous to this one, which I am assuming comes between intro to fourier series and this video. I'm having a very difficult time navigating these fourier videos as they have no listed order and seem to jump around from topic to topic. I'm going to look them up by date I guess..
th-cam.com/play/PLT5_DQAJJLh-ogHjHcLtFYMQy7SkZ7-3i.html
I don't understand how the n just disapears when you integrate at 6:16
u-sub, u=nt du=ndt
I haven't done maths in a while but why is the first integral multiplied by 1/2pi?
Because the formula says so.
Watch the sixth video on Fourier Series Playlist from Khanacademy to find the reason why.
f(t) is some function, that we assume can be written as a series of sin and cos, like:
f(t) = a_0 + a_1 cos(t) + b_1 sin(t) + a_2 cos(2t) + b_2 sin(2t) + ....
So the first term in f(t) is just some constant a_0. If you wanna find a_0, you simply integrate f(t) over the whole period, like:
int_0^2pi f(t) dt = int_0^2pi (a_0 + a_1 cos(t) + b_1 sin(t) + ...) dt = int_0^2pi a_0 dt = 2pi a_0 => a_0 = 1/2pi int_0^2pi f(t) dt
all terms like cos(nt) or sin(nt) is zero when you integrate over the full period. So what's left is just you integrating some constant from 0 to 2pi, and that's where the 2pi comes from.
Tryna learn Fourier series the day before the exam gang wya?
"We definitely need a drum roll" - Sal
why are'nt we using the term b-sub-0 as the first term of the coefficients of sin(mt)?????
ss g it can be anything ... use a zebra if u like
He's doing it that way because you can think of the first b_sub_n*sin(nt) term as b_sub_0*sin(0*t) = 0. It equals zero, which is why he doesn't bother writing it down.
stop it guys....
i got it.....
thanx....
I still don't quite get what n is?
does n have to be integers XD
i get weird answers when n is not an integer XD also is 0 included?
where did the 3 come from
it was the chosen value of the step function. It was 3 from 0 to pi and 0 from pi to 2pi.
this is black magic
please I don't understand where n came in from and why
n is just a number from 1 up until infinity. so when n = 3, that is talking about the third component or third harmonic.
"weighted cosines and sines" means we have a term Ax multiplying cosine or sine. Sure?
Yes...It means that the sines or cosines functions have diferent amplitudes.
where is this from on khan academy?
Electrical engineering series
Everything clicks when your period is in terms of pi. What if it is not? Whole video becomes useless sadly.
I was here
Profs with heavy accents make life horrible for science students. My dad , a very bright man, flunked Calc. for this reason. For todays tuition we deserve better.
Holy hell 😳😲
The expression for a-nought is derived in the preceding video. But the expressions for a-sub-n are not derived, just presented as a formula.
The expression for a-nought is derived in the preceding video. But the expressions for a-sub-n are not derived, just presented as a formula.