musicdsp.org source code archive - WSInf

Audiable alias free waveform gen using width sine (click this to go back to the index)
Type : Very simple
References : Posted by joakim[DOT]dahlstrom[AT]ongame[DOT]com
Notes :
Warning, my english abilities is terribly limited.
How ever, the other day when finally understanding what bandlimited wave creation is (i am a noobie, been doing DSP stuf on and off for a half/year) it
hit me i can implement one little part in my synths. It's all about the freq (that i knew), very simple you can reduce alias (the alias that you can hear that
is) extremely by keeping track of your frequence, the way i solved it is using a factor, afact = 1 - sin(f*2PI). This means you can do audiable alias free
synthesis without very complex algorithms or very huge tables, even though the sound becomes kind of low-filtered.
Propably something like this is mentioned b4, but incase it hasn't this is worth looking up
The psuedo code describes it more.
// Druttis
Code :
f := freq factor, 0 - 0.5 (0 to half samplingrate)
afact(f) = 1 - sin(f*2PI)
t := time (0 to ...)
ph := phase shift (0 to 1)
fm := freq mod (0 to 1)
sine(t,f,ph,fm) = sin((t*f+ph)*2PI + 0.5PI*fm*afact(f))
fb := feedback (0 to 1) (1 max saw)
saw(t,f,ph,fm,fb) = sine(t,f,ph,fb*sine(t-1,f,ph,fm))
pm := pulse mod (0 to 1) (1 max pulse)
pw := pulse width (0 to 1) (1 square)
pulse(t,f,ph,fm,fb,pm,pw) = saw(t,f,ph,fm,fb) - (t,f,ph+0.5*pw,fm,fb) * pm
I am not completely sure about fm for saw & pulse since i cant test that atm. but it should work :) otherwise
just make sure fm are 0 for saw & pulse.
As you can see the saw & pulse wave are very variable.
// Druttis
Comments
from : druttis@darkface.pp.se
comment : Um, reading it I can see a big flaw...
afact(f) = 1 - sin(f*2PI) is not correct!
should be
afact(f) = 1 - sqrt(f * 2 / sr)
where sr := samplingrate
f should be exceed half sr
from : laurent@ohmforce.com
comment :
from : laurent@ohmforce.com
comment : f has already be divided by sr, right ? So it should become :
afact (f) = 1 - sqrt (f * 2)
And i see a typo (saw forgotten in the second expression) :
pulse(t,f,ph,fm,fb,pm,pw) = saw(t,f,ph,fm,fb) - saw(t,f,ph+0.5*pw,fm,fb) * pm
However I haven't checked the formula.
from : 909@gmx.de
comment : Hi Lauent,
I'm new to that DSP stuff and can't get the key to
what'S the meaning of afact? - Can you explain please!? - Thanks in advice!
from : druttis@chello.se
comment : I've been playing around with this for some time. Expect a major update in a while, as soon as I know how to describe it :)
from : druttis@chello.se