Fourier Series Example - Square Wave

Fourier Series Example - Square Wave

        We are going to examine the Fourier Series for a square wave.  The signal we want to work with is given below in Figure 1.

To compute the Fourier Series we use the integrals for the Fourier coefficients.
 
 

We note the following:

• f(t) = A for 0 < t < T/2

• f(t) = -A for T/2 < t < T

First, note that the square wave has odd symmetry so that there are no cosine terms.  Then using the expression for the b's above, we have this expression for b_k.

Evaluating these integrals we have:

First, cancel out the 2/T factor everywhere, and we have:

• b_k = (-A/kp)[cos(kp) - 1 - 1 + cos(kp)]

• And, when k is odd, the two cos(kp) terms add up to -2.

• And, when k is even, the two cos(kp) terms give +2

• The net result is:

• b_k = (4A/kp) when k is odd,

• b_k = 0 when k is even.