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Fourier series understanding problem

  • Thread starter JI567
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  • #1
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Homework Statement


So the question is how does

4/π*(sin(πx))+4/3π *(sin(3πx))+4/5π *(sin(5πx)) = 1

for values of 0<x<1

Homework Equations



No relevant equation needed just don't understand which values of x to take.

The Attempt at a Solution


I am not sure which value of x to start with, it could be anything 0.1 or 0.5, how do I know which x value to start with? I have taken 0.5 and ended up with 1.05 and then taken 0.9 and ended up with 1.15. How the hell does this equal to 1 for any x value?!!!! Please help...
 

Answers and Replies

  • #2
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Homework Statement


So the question is how does

4/π*(sin(πx))+4/3π *(sin(3πx))+4/5π *(sin(5πx)) = 1

for values of 0<x<1

Homework Equations



No relevant equation needed just don't understand which values of x to take.

The Attempt at a Solution


I am not sure which value of x to start with, it could be anything 0.1 or 0.5, how do I know which x value to start with? I have taken 0.5 and ended up with 1.05 and then taken 0.9 and ended up with 1.15. How the hell does this equal to 1 for any x value?!!!! Please help...
You're missing some terms in the series, starting with the sin(7πx) term. Was there a sequence of 3 dots ... in the equation you were given? The three dots indicate an infinite series.

Chet
 
  • #3
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Yeah there were few other terms, the consecutive odd n's, I just didn't write it, sorry! and also yeah sequence of 3 dots so its infinity....but I still don't get it...can you explain how it equals 1...
 
  • #4
19,949
4,106
Yeah there were few other terms, the consecutive odd n's, I just didn't write it, sorry! and also yeah sequence of 3 dots so its infinity....but I still don't get it...can you explain how it equals 1...
Are you familiar with half-wave Fourier series? Or, can you expand the following function in a Fourier series:

y = -1 from x = -1 to x = 0

y = +1 from x = 0 to x = +1

Also, in terms of the series you have written, just try including more terms in the summation (say, up to 20) and see what you get when you evaluate the value at x = 0.5.

Chet
 
Last edited:
  • #5
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Are you familiar with half-wave Fourier series? Or, can you expand the following function in a Fourier series:

y = -1 from x = -1 to x = 0

y = +1 from x = 0 to x = +1

Also, in terms of the series you have written, just try including more terms in the summation (say, up to 20) and see what you get when you evaluate the value at x = 0.5.

Chet
No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!
 
  • #6
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4,106
No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!
I can't know what they ask you to do on your exams.

If the question is, "how well does the three term expression you wrote match y = 1 over the interval 0<x<1?", just plot a graph of the expression as a function of x. Evaluate x every 0.05 over the interval. You can use a spreadsheet to do this type of calculation easily. Then plot the graph. I think you will be surprised at how well it fits over the entire interval with only three terms.

Chet
 
  • #7
LCKurtz
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No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!
More likely they are wanting you to know some of the theory about how a FS represents a function. Have you heard of the Dirichlet conditions? Do you know what the FS does when there is a jump discontinuity in the function? You don't have to literally add the series to know what the sum looks like.
 
  • #8
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Nope I don't....but you could always tell me....
 
  • #9
LCKurtz
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  • #10
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I could, but you can use Google as easily as I can, and you need to read and study a bit about it. One place that pops up on a google search is
http://www.physics.nus.edu.sg/~phylimhs/Fourier3.pdf
Can you explain page 15 please. How did ar just became 4/4 from 2/4? Because in general formula its always Ar = 2/L * etc. Secondly, how are the Ar from 2/4 equal to the one at 4/4. I don't get the integral range, like what they did in that problem
 

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