This series converges to a gaussian filter.This way, I guess that the differentiators can be interpreted as a series of very-small-box filters.
Only for this exam. His courses were quite cool compared to other DSP teachers. It was nice to learn some DSP using CSound and Synoptic's "Virtual Waves" (one of the first virtual synth a long time before VSTis...). This teacher also teached analog and digital electronics (our final year project was a rudimentary but functional analog synth, I think that its schematics are available somewhere on the web). Then he leaved the university and worked with Canam computers, they went bankrupt, then I lost his track.Mr Smith wrote:lol.your DSP teacher sure was an evil guy.
. It is based on a small code by rochebois, but this time I obfuscated it myself 
. Have fun. 
Code: Select all
//sqrfish.cpp
#include <math.h>
#include <stdio.h>
//obfuscation P.Sernine
int main() {float ccc,cccc=0,CC=0,cc=0,CCCC,
CCC,C,c; FILE *CCCCCCC=fopen("sqrfish.pcm",
"wb" ); int ccccc= 0; float CCCCC=6.89e-6f;
for(int CCCCCC=0;CCCCCC<1764000;CCCCCC++ ){
if(!(CCCCCC%7350)){if(++ccccc>=30){ ccccc =0;
CCCCC*=2;}CCC=1;}ccc=CCCCC*expf(0.057762265f*
"aiakahiafahadfaiakahiahafahadf"[ccccc]);CCCC
=0.75f-1.5f*ccc;cccc+=ccc;CCC*=0.9999f;cccc-=
2*(cccc>1);C=cccc+CCCC*CC; c=cccc+CCCC*cc; C
-=2*(C>1);c-=2*(c>1);C+=2*(C<-1); c+=1+2
*(c<-1);c-=2*(c>1);C=C*C*(2 *C*C-4);
c=c*c*(2*c*c-4); short cccccc=short(15000.0f*
CCC*(C-c )*CCC);CC=0.5f*(1+C+CC);cc=0.5f*(1+
c+cc); fwrite(&cccccc,2,1,CCCCCCC);}
//algo by Thierry Rochebois
fclose(CCCCCCC);
return 0000000;}
.
As it can be interpreted as a series of box filters, the resulting frequency attenuation can be interpreted as a sinc()^4 (nota: with its first zero at sr, not sr/2). That would explain this attenuation.Fire Sledge - Ohm Force wrote:I also found an empirical compensation for the volume loss in high freq, but valid up to nyquist/2 : gain /= 1 - step * 1.15;
I came back to rochebois' polynomial algorithm. I am thinking of using it for wavetables. After a while it came to me that the "first order algo" (integral of waveform in the table -> lin interpol -> differenciator) was simply the equivalent of SAT (Summed Area Table) that are used in image synthesis as an alternative to MipMapping.Yes, I think so. Maybe, I can double (or quadruple as in rochebois' sawtooth algorithm) integrate but I am afraid of amplifying digital "noise"...stefancrs wrote:It will give you aliasing if you do it the "summed area" way (integrate the waveform and play the average of it since the last sample instead of playing it's current value), but, you will decrease the aliasing with 6dB / oct (box filtering) compared to the naive implementation, iirc.
and it would require double precision and induce instabilities with fast frequency modulations (as stated before for rochebois's algo). (even if I cannot guess how to do this for the double integration version ). I will have a busy easter weekend. 
Just use linear-phase BLEPs (unlike what the original paper claims, minimum-phase just adds problems without solving any). To reduce cache line fetches reorder your BLEP table such that every single "branch" is a continuous array of samples (instead of striped into every Nth sample). That said, I'm not convinced there's anything to be gained from SIMD here.0xFF wrote:5 years later, what is the most common use method to generate a band-limited sawtooth ? I am searching for a method that is suitable for SIMD implementation.
I have used minBLEP method which was OK (also for hard-synchronization), but this requires reading thru a table which is difficult for me to use with SIMD. Maybe I am missing something ...
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