Hi All,

Lets say we want to calculate the Complex Fourier Series Coefficients of a signal. Lets say this signal is periodic with T=2.
Its signal looks like this

http://i396.photobucket.com/albums/pp47/ohwcomp/Q1.jpg


Looks like a sawtooth signal but with no negative bit. How do I express this signal x(t) = ?

Then how do I calculate these Complex Fourier Series Coefficients? Im really stuck and not too sure on the theory either. I understand that the signal can be expressed a sum of two sinusoids etc that have the same fundamental frequency which is a multiple of the period. Thus using Eulers formula can be written in phasor form but where do I go from here?

Thanks in advance!

 

Hi,

x(t) must be expressed as a piecewise function. So,

 x(t) = { 0 ; -1 < t < 0
        { 2t ; 0 < t < 1 (line eqn)

Then, you need to plug this into the complex fourier formulae and integrate with limits at the discontinuities. Here's an example

http://ocw.mit.edu/NR/rdonlyres/Mec...85F-A68D-433B-BAE3-CDE7BA342115/0/lect_12.pdf

Goodluck,

Steve

 

Thanks for the info Steve, currently working on a solution for that problem.

I have another question if anyone can help me please.

I can find out the fundamental frequency by using the f = 1/T.
I understand that the power spectrum is different than the magnitude spectrum ie that it is squared.
Im a little confused how to interpret these graphs to get the frequencies and phase components, and into what kind of form or expression to get this output signal.

What is the ouput signal form? Is it a sum of sinusoids? Similar to the Q1 asked above?

Thanks again!

 

Can anyone help please on both questions?

Does the sqaure wave have a fundamental frequency of 2KHz with harmonic frequencies 5KHz 10KHz etc. ie for k = 1,3,5 etc.

 

I don't have much time to spent here, so I found some old assignment solutions that might help. Hope it helps