Fourrier example

Fourier series

• A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines.

• The computation Fourier series is known as harmonic analysis

• a way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually

• then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired or practical.

Fourrier example

We will set the values as follows: A = 4 volts, T = 1 second. Also, it is given that the width of a single pulse is T/2. Find the rectangular Fourier series of this signal?

• First, we can see clearly that this signal does have a DC value: the signal exists entirely above the horizontal axis.

• Next, we can see that if we remove the DC component (shift the signal downward till it is centered around the horizontal axis), that our signal is an odd signal.

• This means that we will have an terms, but no bn terms.

1. DC value (must calculate a0 )

2. Its an Odd Function so (bn = 0 for n > 0)

Bn =0 for all n>0

3. Calculate an

F(t)= 0 for 0 >t>-t/2

4 for 0<t< t/2