Construct the first three fourier approximations to the square wave function: f(x) =-1 [-pi,0)1 [0,pi)

Step-by-step explanation:

The given square wave function is:

.

The Fourier series approximation on the interval;



is given by;



where



We can see from the graph that, the square wave function is odd on the given interval.

This implies that;





The product of an odd function and an even function gives an odd function.

This implies that;



Also,











We substitute these values into the above formula to get;



To construct the first three Fourier approximation we substitute



The first three approximations are;