filter design - code problem

[kaj]

Hello.
***************************
prewarped freq = 2/T*tan(2*pi*freq*T/2), where T is sample time.
***************************
when cutoff freq = 5000 and T= 1/44100, then
prewarped freq = 32815.591 (which is the actual input value)

H(z) =

0.0174349 + 0.0523047z^-1 + 0.0523047z^-2 + 0.0174349z^-3
-----------------------------------------------------------------------------------------
1 - 1.8823263z^-1 + 1.4150742z^-2 - 0.3932688z^-3

legendrefilter5000.osm

lengendre filter cutoff 5000hz

(8.71 KiB) Downloaded 82 times

[MegaHurtz]

I ment that the z transform would be differentiating, given that multiplying a differentiated result would create a filter. And multiplying an integrated signal would create gain. So i wasnt able to see where it would get integrated again. Wich would be needed somewhere..

[kaj]

I generalized the filter. Maybe It's OK.

Code: Select all

streamin in;
streamin wo;
streamout out;
float x0, x1, x2, x3;
float y0, y1, y2, y3;
float a, b, c, d, e, f, g, r;
float w, ww, www;

w = 2*44100 * tan1(0.5*wo/44100); // prewarping the digital freq
ww = w * w;
www = ww * w;

r = (99316848847*www+20618754192943200*ww+1753981684186662000000*w+118029161812506173712000000);
a = (297950546541*www+20618754192943200*ww-1753981684186662000000*w-354087485437518521136000000);
b = (297950546541*www-20618754192943200*ww-1753981684186662000000*w+354087485437518521136000000);
c = (99316848847*www-20618754192943200*ww+1753981684186662000000*w-118029161812506173712000000);
a = a/r;
b = b/r;
c = c/r;
d = 99316848847*www/r;
e = 297950546541*www/r;
f = 297950546541*www/r;
g = 99316848847*www/r;

x0 = in;
y0 = -1*a*y1 - b*y2 - c*y3 + d*x0 + e*x1 + f*x2 + g*x3;
y3 = y2;
y2 = y1;
y1 = y0;
x3 = x2;
x2 = x1;
x1 = x0;
out = y0;


legendre_general.osm

legendre generalized

(15.55 KiB) Downloaded 84 times

[tor]

I'll try and find the ported rbj thread as the example you gave me isnt loading.
the 64bit stuff seems . . useless? if you can only feed it 32 bit values then round them back off to 32 bit at the end . .

ok?
lets just say that numbers with one decimal represent 32 bit and two decimal represent 64 bit
in 64 bit with conversion after calculations:
1.2*1.2+1.2*1.2=1.44+1.44=2.88≃2.9 (0.02 in diff)
in 32 bit with no conversion:
1.2*1.2+1.2*1.2=1.4+1.4=2.8 (0.08 in diff)

as you can see there is a huge difference and in a feedback structure theese errors build up quickly

[firmament]

I've done a few ports of kaj's code to get them working in synthmaker. however because of precision issues, they arent accurate below ~300hz and break down completely sub-50

3-opt-l-filters.osm

(4.09 KiB) Downloaded 75 times

the explicit one is the full unoptimised code. asm optimised, it uses >20 cycles. the 64bit version is more accurate (thanks for the tip tor) but the difference isn't very significant

[MegaHurtz]

It ougta be 64 bits when it runs 64 bits

[tor]

You are very welcome

Measurements I have done with the 2-pole biquads in VST Plugin Analyser shows a difference in prox -50dB for the noise floor. And in the bass area the altered frequencies sounds more clean and clear. But I totally agree that it should be possible to do all of the calculations in 64 bit. The speed of the digital revolution makes me think we soon will see plugs prosessing at 128 bit

But they are probably not going to be created in SM

[infuzion]

asm optimised, it uses >20 cycles.

3p Opt-L ASM2 is missing links from the green to the ASM. I assume connect in the order of the last math item?

[firmament]

asm optimised, it uses >20 cycles.

3p Opt-L ASM2 is missing links from the green to the ASM. I assume connect in the order of the last math item?

yeah, theyre arranged so the column of multiplies on the far right of the green mess are in the same descending order as the coefficient inputs of the asm.

In case anyone was dying to know, the filter is the "optimum" midpoint between chebyshev and butterworth, giving the steepest cutoff possible without ripple

[MegaHurtz]

^^ Also getting a bit steeper as it drops into infinity.

[firmament]

ok?
lets just say that numbers with one decimal represent 32 bit and two decimal represent 64 bit
in 64 bit with conversion after calculations:
1.2*1.2+1.2*1.2=1.44+1.44=2.88≃2.9 (0.02 in diff)
in 32 bit with no conversion:
1.2*1.2+1.2*1.2=1.4+1.4=2.8 (0.08 in diff)

as you can see there is a huge difference and in a feedback structure theese errors build up quickly

haha should have thought it through before I posted really and i see how 128 bit could be useful.. not sure how to get this filter to work otherwise.

attached is a minor fix, the green stuff was missing quite a bit in the asm version so ive cleared that up