Fourier Series for a Square-wave Function

[K.QMUL]

Homework Statement

Consider the square wave function defined by y(t) = h (constant) when 0 ≤ (t + nT) ≤1,
y(t) = 0 elsewhere, where T = 2 is the period of the function. Determine the Fourier series
expansion for y(t).

Homework Equations

Fourier Analysis Coefficients

The Attempt at a Solution

Please look at the attachment, I am not convinced I have done it right so far... please help.

 

[jbunniii]

Your answer for $A_n$ can be simplified. Since $T=2$, it becomes
$$A_n = \frac{h}{\pi n} \sin(\pi n)$$
Now what is $\sin(\pi n)$?

 

[jbunniii]

By the way, you can save yourself some work as follows. Note that if we define $x(t) = y(t) - h/2$, then $x$ is an odd function. What can you say about the Fourier series of an odd function? And how does the Fourier series of $x$ relate to the Fourier series of $y$?