 Fourier series of a periodic rectangular pulse

An even train of rectangular pulses of width $w<T$, period $T$ and unit area per pulse has Fourier coefficients $a_n=(2/T)\mathrm{sinc}(\pi nw/T)$ for $n\ge 0$. Here the sinc function is normalized as $\mathrm{sinc}z=\sin z/z$, and the constant contribution is $a_0/2=1/T$. Integrating the cosine over the pulse proves the formula; evenness eliminates the sine coefficients. At a pulse edge, pointwise convergence of a piecewise smooth Fourier series gives the mean of the one-sided values rather than a prescribed endpoint value.