musicdsp.org source code archive - WSInf

Fast sine and cosine calculation (click this to go back to the index)
Type : waveform generation
References : Lot's or references... Check Julius O. SMith mainly
Code :
init:
float a = 2.f*(float)sin(Pi*frequency/samplerate);
float s[2];
s[0] = 0.5f;
s[1] = 0.f;
loop:
s[0] = s[0] - a*s[1];
s[1] = s[1] + a*s[0];
output_sine = s[0];
output_cosine = s[1]
Comments
from : nigel
comment : This is the Chamberlin state variable filter specialized for infinite Q oscillation. A few things to note:
Like the state variable filter, the upper frequency limit for stability is around one-sixth the sample rate.
The waveform symmetry is very pure at low frequencies, but gets skewed as you get near the upper limit.
For low frequencies, sin(n) is very close to n, so the calculation for "a" can be reduced to a = 2*Pi*frequency/samplerate.
You shouldn't need to resync the oscillator--for fixed point and IEEE floating point, errors cancel exactly, so the osciallator runs forever without drifting
in amplitude or frequency.
from : DFL
comment : Yeah, this is a cool trick! :)
FYI you can set s[0] to whatever amplitude of sinewave you desire. With 0.5, you will get +/- 0.5
from : bigtick@pastnotecut.org
comment : After a while it may drift, so you should resync it as follows:
const float tmp=1.5f-0.5f*(s[1]*s[1]+s[0]*s[0]);
s[0]*=tmp; s[1]*=tmp;
This assumes you set s[0] to 1.0 initially.
'Tick
from : DFL
comment : Just to expalin the above "resync" equation
(3-x)/2 is an approximation of 1/sqrt(x)
So the above is actually renormalizing the complex magnitude.
[ sin^2 (x) + cos^2(x) = 1 ]
from : antiprosynthesis@hotmail.com
comment : I made a nice little console 'game' using your cordic sinewave approximation. Download it at
http://users.pandora.be/antipro/Other/Ascillator.zip (includes source code). Just for oldschool fun :).
from : wink@op.pl
comment : what da shit is this? i don't know why it is so interesting?
from : hplus
comment : Note that the peaks of the waveforms will actually be between samples, and the functions will be phase offset by one half sample's worth.
If you need exact phase, you can compensate by interpolating using cubic hermite interpolation.