Kurt's Assignment

Common Synthesizer Waveforms

Square Wave

$x(t)=x(t+T)=a_0+\sum _{n=1}^{\mathrm{\infty }}{a}_n\cos (n{\omega }_{0}t)+b_n\sin (n{\omega }_{0}t)$

$\begin{array}{rl}{a}_0& =\frac{1}{T}\underset{0}{\overset{T}{\int }}f(t)dt\\ & =\frac{1}{T}\underset{0}{\overset{\frac{1}{2}T}{\int }}Hdt+\frac{1}{T}\underset{\frac{1}{2}T}{\overset{T}{\int }}0dt\\ & =\frac{1}{T}[Ht]\end{array}$