Understanding Fourier Series: Finding f(t)

[EugP]

Hi,

I am having trouble understanding how to use Fourier series. To be more specific, here's what I mean.

My question about those formulas is, how do I know what f(t) is?
When I do excercises, I never get what f(t) is. Can anyone tell me how to find it?

 

[cristo]

Isn't f(t) the function for which you are attempting to find a Fourier series expansion?

 

[EugP]

Isn't f(t) the function for which you are attempting to find a Fourier series expansion?

Yes, but in excersies that I've tried doing, I am not told f(t). I only get a graph usually.

 

[cristo]

Yes, but in excersies that I've tried doing, I am not told f(t). I only get a graph usually.

Can you not spot an equation for the graph? Why don't you post an example, and it'll be easier to help.

 

[EugP]

Can you not spot an equation for the graph? Why don't you post an example, and it'll be easier to help.

Yes, here is one of the excersises. I need to find the Fourier series of that function:

 

[Integral]

Use the graph to define your f(t). This called a piecewise function, it means you will need to break the integrals into pieces which correspond to the different parts of the function.

0 <= t < 50 f(t) = 40
50 <= t < 100 f(t) = 80
100 <= t < 150 f(t) = -40
150<= t <200 f(t) = -80

Now simply evaluate the integrals, using the different segments as that limits for each section.

 

[EugP]

Use the graph to define your f(t). This called a piecewise function, it means you will need to break the integrals into pieces which correspond to the different parts of the function.

0 <= t < 50 f(t) = 40
50 <= t < 100 f(t) = 80
100 <= t < 150 f(t) = -40
150<= t <200 f(t) = -80

Now simply evaluate the integrals, using the different segments as that limits for each section.

Alright, so I took your advice, but my results are still wrong. Here's what I did:

$$a_v=\frac{1}{T}\int{f(t)dt}$$
$$a_v=\frac{1}{50}\int{40dt}$$
from 0 to 50, and I got 40, but the answer is 0.

EDIT: The answer I got was correct, I just didn't finish. Thank you cristo and Integral for your help.