Hi, Julius.
Yes, I was a bit surprised to see NANs in the last case because I've read a
lot about how zero-delay feedback filters perform well for the entire
spectrum, but I guess it must only to true for first-order filters. I'll do
more testing later.
Ciao,
Dario
On Mon, 21 Dec 2020 at 04:47, Julius Smith <julius.sm...@gmail.com> wrote:
> Hi Dario,
>
> Those numbers look good except for the NaNs in the last case.
>
> - Julius
>
> On Sun, Dec 20, 2020 at 7:12 PM Dario Sanfilippo <
> sanfilippo.da...@gmail.com> wrote:
>
>> Hi, Julius and Oleg.
>>
>>
>>> The question remains as to which filter form is more accurate.
>>>
>>> Another thing worth mentioning, by the way, is that tf2snp can be
>>> modulated, even using white noise for its coefficients, without affecting
>>> signal energy.
>>> That's the usual and original principal benefit of going to the
>>> normalized ladder form - "power-invariant modulatability".
>>> The superior numerical robustness for closely spaced poles was observed
>>> later and documented in the literature by Gray and Markel, as I recall.
>>>
>>> - Julius
>>>
>>
>> Below we have a simple test to see how much the filters diverge from the
>> expected 1/sqrt(2) attenuation at cut-off. The filters are tested with 12
>> frequencies, the first 12 octaves starting at ~15.85 Hz.
>>
>> The values show the attenuation error in dBs. I'm calculating the RMS
>> with an.rms_envelope_tau(10) for a steady RMS calculation and I'm taking
>> the values after a thousand seconds to be sure that the RMS filters are
>> fully charged. I did the test at 96kHz SR, double precision.
>>
>>
>> We have: highpass(2), snp, svf_oleg, svf_zava. At least for the audible
>> spectrum, they all seem to perform pretty well. Hard to tell which one is
>> best for the time-invariant case, isn't it?
>>
>> Ciao,
>> Dario
>>
>> 15.8489323,
>>
>> 0.0035875327635620513,
>>
>> 0.0035875324371487105,
>>
>> 0.0035875327635620513,
>>
>> 0.0035875327636175625,
>>
>> 31.622776,
>>
>> 0.0013189248524392294,
>>
>> 0.0013189248481326743,
>>
>> 0.0013189248529810182,
>>
>> 0.0013189248528688857,
>>
>> 63.0957336,
>>
>> -0.00014836658605854591,
>>
>> -0.00014836659250561102,
>>
>> -0.00014836658607297881,
>>
>> -0.00014836658600858588,
>>
>> 125.89254,
>>
>> -0.00029188057887152841,
>>
>> -0.00029188057380447052,
>>
>> -0.00029188057895590536,
>>
>> -0.00029188057892148844,
>>
>> 251.188644,
>>
>> 0.00010734229401176965,
>>
>> 0.00010734229400843898,
>>
>> 0.00010734229401621054,
>>
>> 0.00010734229399067541,
>>
>> 501.187225,
>>
>> -0.0001285532826483804,
>>
>> -0.00012855328314131942,
>>
>> -0.00012855328263283727,
>>
>> -0.00012855328265393151,
>>
>> 1000,
>>
>> -2.7386120134975656e-05,
>>
>> -2.7386120134975656e-05,
>>
>> -2.7386120134975656e-05,
>>
>> -2.7386120134975656e-05,
>>
>> 1995.26233,
>>
>> 5.9325435514123726e-06,
>>
>> 5.9325435203261279e-06,
>>
>> 5.9325435536328186e-06,
>>
>> 5.9325435569634877e-06,
>>
>> 3981.07178,
>>
>> 1.4404616551222382e-05,
>>
>> 1.4404616547891713e-05,
>>
>> 1.4404616545671267e-05,
>>
>> 1.4404616547891713e-05,
>>
>> 7943.28223,
>>
>> -1.0056763050103612e-06,
>>
>> -1.0056763061205842e-06,
>>
>> -1.0056763072308073e-06,
>>
>> -1.0056763061205842e-06,
>>
>> 15848.9316,
>>
>> -1.1356025741982023e-05,
>>
>> -1.1356025744202469e-05,
>>
>> -1.13560257408718e-05,
>>
>> -1.1356025743092246e-05,
>>
>> 31622.7773
>>
>> nan,
>>
>> 173.00064800561148,
>>
>> nan,
>>
>> nan
>>
>>
>>>
>>>
>>> On Sun, Dec 20, 2020 at 12:07 PM Oleg Nesterov <o...@redhat.com> wrote:
>>>
>>>> On 12/20, Dario Sanfilippo wrote:
>>>> >
>>>> > > --- a/filters.lib
>>>> > > +++ b/filters.lib
>>>> > > @@ -1004,7 +1004,7 @@ declare tf2np copyright "Copyright (C)
>>>> 2003-2019 by
>>>> > > Julius O. Smith III <jos@ccr
>>>> > > declare tf2np license "MIT-style STK-4.3 license";
>>>> > > tf2np(b0,b1,b2,a1,a2) = allpassnnlt(M,sv) : sum(i,M+1,*(tghr(i)))
>>>> > > with {
>>>> > > - smax = 0.9999; // maximum reflection-coefficient magnitude
>>>> allowed
>>>> > > + smax = 0.999999999; // maximum reflection-coefficient magnitude
>>>> allowed
>>>> > > s2 = max(-smax, min(smax,a2)); // Project both
>>>> reflection-coefficients
>>>> > > s1 = max(-smax, min(smax,a1/(1+a2))); // into the defined
>>>> > > stability-region.
>>>> > > sv = (s1,s2); // vector of sin(theta) reflection coefficients
>>>> > >
>>>> > >
>>>> > If I'm not wrong, anything above 0.9999999 would be rounded to 1 in
>>>> single
>>>> > precision, right?
>>>>
>>>> Quite possibly, I didn't even bother to check.
>>>>
>>>> In case it was not clear, I didn't try to propose a fix, I just tried to
>>>> identify where does the problem come from.
>>>>
>>>> > Would it be possible to choose different constants based on different
>>>> > options given to the compiler?
>>>>
>>>> Yes, perhaps we should use singleprecision/doubleprecision I dunno.
>>>> (Can't
>>>> resist I think this feature was a mistake but this is offtopic ;)
>>>>
>>>> Even if we forget about single precision, I simply do not know how much
>>>> we can enlarge this limit. The 0.999999999 value I used is just the
>>>> "random
>>>> number closer to 1".
>>>>
>>>> > If not, a philosophical question (not really) for these situations
>>>> might
>>>> > be: should we prioritise single precision or double precision
>>>> > performance/stability?
>>>>
>>>> Good question! please inform me when you know the answer? ;)
>>>>
>>>> Oleg.
>>>>
>>>>
>>>
>>> --
>>> "Anybody who knows all about nothing knows everything" -- Leonard
>>> Susskind
>>>
>>
>>
>> --
>> Dr Dario Sanfilippo
>> http://dariosanfilippo.com
>>
>
>
> --
> "Anybody who knows all about nothing knows everything" -- Leonard Susskind
>
--
Dr Dario Sanfilippo
http://dariosanfilippo.com
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