Finding the harmonic function of a function?

[YeeHaa]

Hello everyone,

Since I needed some place to ask my question, I ended up here. I sure hope you can help me :).

I'm "completely" new to Signals & Systems, and although I'm new to it, I already have loads of assignments I need to make (note this is NOT homework!, they are to make me understand S&S..., if this is interpreted as HW, my apalogies). The problem is I don't really understand how some of the formulas work or what steps I need to take...

The book I'm using: Signals & Systems by M.J. Roberts

The question:

Given : The function t(u(t-2) - u(t-5)) is periodically expanded with period 9.

Find the harmonic function, using the fundamental period as base period.
The formule that I'm supposed to use is:

I could also find this harmonic function by using the appendix E in the book (second question).

My questions:
Graphical expression: I know the function exists out of a substraction of two unit step functions, multiplied with "t"? I'm not sure how to picture the function in total?

Could anyone give me a head start, or help me explain how I integrate this function in the formula?

 

[LCKurtz]

T = 9. Your graph is identical to f(t) = t between 2 and 5 and zero elsewhere on the interval (0,9). Then extended periodically. So break your integral from 0 to 9 into three parts, two of which are very easy.

 

[YeeHaa]

Then I get this as my function:

[PLAIN]http://img577.imageshack.us/img577/5808/function.jpg

Is this solution done the right way? I have the feeling I messed up somewhere...

[PLAIN]http://img824.imageshack.us/img824/2446/function2.png

If it is right, do I just let k be a chosen integer?

Thanks for your help so far.

 

[LCKurtz]

I didn't check all your steps. But you do have the function right and the integral set up correctly. And it does look like you dropped an f_F along the way.

I'm not an EE so am unfamiliar with Signals & Systems. And I'm guessing that what you refer to as the "harmonic function" is what I would call the Fourier Series.

Anyway, barring other arithmetic mistakes, it looks good to me.

 

[YeeHaa]

The formula is a formula given in the section 'Fourier series', so I would presume that is correct.

My question really was if the arithmetic was correct? The f_F is (1/9), and i integrated that.

Hope someone can help me.

Thanks.

 

[YeeHaa]

Assuming the integral output is correct, I'm not sure what to do with X[k] afterwards so I can find the harmonic of the function?