# fourier series

#### hamza324

Joined Jul 10, 2011
33
I am trying to solve fourier series problems. i have few confusions about that..

1) x(t) =$$\sum c_x(k)e ^{jkwt}$$

where as $$c_x(k) = \int_T x(t) e^{-jwt} dt$$

My question is that when which equation do we use to plot the graph.
and how do we take the values for the graph. Is it BODE PLOTS or is it simply plugging in the values.

suppose i havethis expression
$$c_x(k)= A/2 \frac {cos(k\prod-1)}{k\prod}^2$$

$$or\ i\ have\ c_x(k)= A/2 \frac {sinc(k\prod-1)}{k\prod}^2$$

then how can i graph this equation for $$c_1\ ,\ c_2\ ,\ ......$$

#### Georacer

Joined Nov 25, 2009
5,182
Are these equations for $$c_x(k)$$ correct? The multiplication symbol has no argument in either of them. It refers to the product of what?

#### hamza324

Joined Jul 10, 2011
33
The question i have is f(t)= $$A\ cos200\pi t$$
and this is the expression for fourier series $$x(t) = \sum^{+\infty}_{k=-\infty}c_ke^{j2wkt}$$

i got the following solution for fourier coefficients

$$now\ for\ c_k\ =-\frac{1}{4}\frac{Sin(\pi +k)(0.5)}{(\pi+k)}-\frac{1}{4}\frac{Sin(\pi - k)0.5}{\pi-k}-\frac{1}{4}\frac{Sin(\pi+k)1.5}{\pi+k}-\frac{1}{4}\frac{Sin(\pi-k)1.5}{\pi-k}$$

Now my prof asks me to sketch the fourier series coefficients i.e. $$c_k\ for\ k=\ 1,2,3,....$$

I wanna know how to sketch the result i got