# Homework Help: Fourier Series for a Square-wave Function

1. Dec 10, 2013

### K.QMUL

1. The problem statement, all variables and given/known data

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).

2. Relevant equations

Fourier Analysis Coefficients

3. The attempt at a solution

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2. Dec 10, 2013

### 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 $\sin(\pi n)$?

3. Dec 10, 2013

### 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 $y$?