Kurt's Assignment

Common Synthesizer Waveforms

Square Wave

$x(t)=x(t+T)=a_{0}+\sum _{n=1}^{\infty }a_{n}\cos(n\omega _{0}t)+b_{n}\sin(n\omega _{0}t)$

${\begin{aligned}a_{0}&={\frac {1}{T}}\int _{0}^{T}f(t)dt\\&={\frac {1}{T}}\int _{0}^{{\frac {1}{2}}T}Hdt+{\frac {1}{T}}\int _{{\frac {1}{2}}T}^{T}0dt\\&={\frac {1}{T}}[Ht]\end{aligned}}$