Although widely hated and feared by sound engineers, feedback and distortion lie at the heart of most hardware and software synthesis algorithms. Without them there would be no electronic music. With care and knowledge, they can be used to make a wide array of oscillators, semi-periodic and chaotic signal generators, filters, dynamic processors, reverberators, and more.
Topics (may change slightly):
1. waveshaping. Algebraic treatment. Trig formulae. Pulses. good and bad fuzz. even and odd waveforms. FM as distortion. "bias"
2. nonlinear distortion in the complex plane
3. linear discrete-time feedback. classical reverberator design.
4. linear and non-linear digital filters AGC and companding slew generators
5. nonlinear reverberators and AGC- or distortion-limited feedback with delay
6. feedback in continuous time Predator/prey (Bendixson) theorem; sawtooth oscillator; Lorentz attractor; numerical solutions to ODEs; classical waveforms crackle box. classical Moog filter
7. control theory, classical and with delay
8. nonlinear coupling between oscillators
9. feedback in rooms (examples, Lucier and Collins).
10. nonlinearity and feedback in video and graphics
Here are blackboard images and patches and videos.