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Fast sine wave calculation

Type : waveform generation
References : James McCartney in Computer Music Journal, also the Julius O. Smith paper

Notes :
(posted by Niels Gorisse)
If you change the frequency, the amplitude rises (pitch lower) or lowers (pitch rise) a LOT I fixed the first problem by thinking about what actually goes wrong. The answer was to recalculate the phase for that frequency and the last value, and then continue normally.

Code :
ip = phase of the first output sample in radians
w = freq*pi / samplerate
b1 = 2.0 * cos(w)


y0 = b1*y1 - y2
y2 = y1
y1 = y0

output is in y0 (y0 = sin(ip + n*freq*pi / samplerate), n= 0, 1, 2, ... I *think*)

Later note by James McCartney:
if you unroll such a loop by 3 you can even eliminate the assigns!!

y0 = b1*y1 - y2
y2 = b1*y0 - y1
y1 = b1*y2 - y0


Added on : 22/04/03 by kainhart[at]hotmail[ DOT ]com
Comment :
try using this to make sine waves with frequency less that 1. I did and it gives very rough half triangle-like waves. Is there any way to fix this? I want to use a sine generated for LFO so I need one that works for low frequencies.

Added on : 24/10/06 by asynth[ AT ]io[ DOT ]com
Comment :
looks like the formula has gotten munged.
w = freq * twopi / samplerate

Added on : 28/08/13 by joi[ AT ]nea[ DOT ]ufsc[ DOT ]br
Comment :
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