[PD] OT : using libre office for data regression; WAS Re: efficient approximation of trig functions for hi pass formula (was: could vanilla borrow iemlib's hi pass filter recipe?)
cyrille henry
ch at chnry.net
Thu Oct 20 10:26:01 CEST 2016
Le 20/10/2016 à 01:07, katja a écrit :
[...]
>>
>>> For the filter recipe the curve must go through coordinates [0 1] and
>>> [pi -1], to get the expected behavior when cutoff frequency is set to
>>> DC or Nyquist. [hip~ 0] should not block DC, which is only possible
>>> when the coefficient is exactly 1 like you get it with
>>> (1-sin(0))/cos(0). I tuned my factors 'by hand' to do so. That may be
>>> possible with your libre office result as well.
>>
>> yes, in my example the result is slightly different from 1 / -1.
>> i tried again, adding about 20 points for X=0 and X=1 to get more weight for
>> this coordinate.
>> the coef where better, but not perfect.
>>
>> still it's a good starting point for manual adjustment.
>
> That's what I thought, avoiding the initial guess iterations saves a
> lot of time. Can you post your adjusted parameters? Being an
> approximation the function will never be perfect. We can select the
> best frequency response compromise.
libre office say :
-1.5743519661 X
-1.1794365231 X^3
-2.0916936873 X^5
(for X between -0.5 / 0.5)
>> However, when done in
>>>
>>> double precision the calculation will give slightly different result.
>>> Above or below 1, I don't know yet. In any case this has to be
>>> considered when writing the C.
>>
>> shouldn’t it be clipped? (what is a filter with negative frequency, or
>> frequency above Nyquist?)
>
> Yes coefficients below -1 and above 1 must be clipped. But what if it
> doesn't reach 1 at DC or -1 at Nyquist in double precision because of
> the rounding difference. The behavior at those extremes would be
> incorrect. Not that it matters now, we don't have double precision pd.
> But code written today should be double-precision-proof, you never
> know what will happen tomorrow.
since we know that aX + bX³ + cX⁵ should be 1 for X = -0.5, we can automatically adjust "a" to:
a = 1 - b*0.5³ - c*0.5⁵
using only b and c from the polynomial regression.
(since the function is odd, it will also work for X = 0.5)
I did not try, but apart from rounding error, it should satisfy the extreme condition whatever precision is used, as long as "a" is computed in the C code.
(the pi value I used in libreoffice is not double precision accurate anyhow).
cheers
c
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