SawDPW super-efficient sawtooth oscillator with low aliasing

SawDPW.ar(freq, iphase, mul, add)

A sawtooth oscillator using the "Differentiated Parabolic Wave" technique, which suppresses aliasing at a wide range of frequencies, yet is about 3 times as CPU-efficient as SuperCollider's Saw ugen. 

freq - frequency in Hertz

iphase - initial phase offset, a value ranging from -1 to 1.

It doesn't guarantee to be alias-free but sounds very good for most applications: e.g. at 44.1 kHz sample rate, aliasing can only be heard if the frequency goes over around 4 kHz. The technique is documented in Välimäki (2005) Signal Processing Letters 12(3) pages 214-217.

See also: PulseDPW

Server.default = s = Server.internal;

s.boot

s.scope

// Amplitude will be polled, move mouse to change frequency

{var x; x = SawDPW.ar(MouseX.kr(50, 2000, 1));Amplitude.ar(x, 0.2, 0.2).poll; x.madd(0.1).dup}.play

{var x; x = SawDPW.ar(K2A.ar(MouseX.kr(50, 2000, 1)));Amplitude.ar(x, 0.2, 0.2).poll; x.madd(0.1).dup}.play

// Listen to these to compare aliasing characteristics

{var x; x = SawDPW.ar(MouseX.kr(50, 10000, 1).poll); x.madd(0.1).dup}.play

{var x; x = Saw   .ar(MouseX.kr(50, 10000, 1).poll); x.madd(0.1).dup}.play

{var x; x = LFSaw .ar(MouseX.kr(50, 10000, 1).poll); x.madd(0.1).dup}.play

{var x; x = [SawDPW, Saw].collect(_.ar(K2A.ar(MouseX.kr(10, 20000, 1).poll))); Amplitude.ar(x[0], 0.2, 0.2).poll; x.madd(0.1)}.play

// Efficiency comparisons:

~num = 100;

// scsynth on PPC Mac G4, idle around 2.1% CPU

// k-rate freq inputs

{Saw   .ar({exprand(50, 1000)}.dup(~num)).mean.dup}.play // 30.7% CPU

{SawDPW.ar({exprand(50, 1000)}.dup(~num)).mean.dup}.play // 12.4% CPU

{LFSaw .ar({exprand(50, 1000)}.dup(~num)).mean.dup}.play //  7.0% CPU