# Fourier series understanding problem

• JI567
Can you explain page 15 please. On page 15, in the paragraph titled "Fourier Series and the Convolution Theorem", the author references the Convolution Theorem. The Convolution Theorem states that if you have a function and a second function that are both Fourier series, then the two functions are related by a convolution. In summary, the author is saying that if you have a function and a second function that are both Fourier series, then the two functions are related by a convolution.f

## 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...

## 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

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...

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:
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!

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

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.

Nope I don't...but you could always tell me...

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