Digression: some common functions

Subtractive synthesis basis waveforms (sine, square, saw, triangle, pulse)

 ‐the basic spectra
 ‐the effects of duty cycle modulation (PWM)

Noise (white, brown, pink, 1/f, S/H)

 ‐power spectra but not real spectra!
 ‐difference between ordinary deterministic signals and stochastic phenomena!

Amplitude modulated signals

 ‐symmetrical sidebands
 ‐DSB/SSB/VSB and likeness to radio transmission

Chebyshev polynomials

Possibility of shaping sines into any periodic function!

Waveshaped signals

Generalization via Chebyshev polynomials and intermodulation products

Bessel functions

 ‐connection to FM
 ‐these are of little use by themselves

Frequency modulated signals

 ‐sidebands behave according to first order Bessel functions, why? (diff. equs?)

Splines (cubic B‐splines, NURBS)

 ‐for interpolation and control, not synthesis ⇒ no need for spectra

Window and glue functions

 ‐again smoothess is important
 ‐for window functions spectra as these are needed in convolution estimates (windowing!) and WFS/granular