Fast sine wave calculation

  • Author or source: James McCartney in Computer Music Journal, also the Julius O. Smith paper
  • Type: waveform generation
  • Created: 2002-01-17 00:52:33
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.
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Variables:
ip = phase of the first output sample in radians
w = freq*pi / samplerate
b1 = 2.0 * cos(w)

Init:
y1=sin(ip-w)
y2=sin(ip-2*w)

Loop:
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

Comments

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.

looks like the formula has gotten munged.
w = freq * twopi / samplerate