# [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
Wed Oct 19 18:32:35 CEST 2016

```
Le 19/10/2016 à 17:34, katja a écrit :
> Thanks for your update Cyrille. This seems a useful approach to find
> approximations. I should really learn how to do that with libre
> office. Do you have tutorial links? So far I found this:
> https://newtonexcelbach.wordpress.com/2015/06/28/using-linest-for-non-linear-curve-fitting-examples-hints-and-warnings/.

I  learn to do this yesterday...
Most informations I found on the web was outdated, but it's very simple.
for short :
create 2 column with X/Y data.
select the data.
click insert / diagram. select X/Y dispersion, in order to draw a X/Y graph of your data.
then double click on the diagram and click on the curve to select it.
then right click and "insert a tendency curve"
then enjoy all option available.
(there is no "odd only polynomial", but even value was almost 0 in the last example).

Don't forget to click "draw the equation"
The only problem is that i did not find a way to cut/paste the equation...

(my libre office is in french, so menu translation may not be accurate)

> 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.

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?)

cheers
c

>
> Katja
>
> On Wed, Oct 19, 2016 at 4:18 PM, cyrille henry <ch at chnry.net> wrote:
>> since you manually adjust the coefficient, i wanted to see the difference
>> with coefficient adjusted/optimised by a computer.
>> I update the calc  using X from -0.5 to 0.5 with X = (x-0.5)*Pi
>> The coefficient i get are really different from yours (when considering the
>> Pi factor between them).
>>
>> I update you patch with this coefs.
>> I don't understand why, but your coefs works better for low frequency.
>> so, nothing better here, but I still think it's worth sharing, in case i'm
>> not the only one wondering...
>>
>>
>> also, there was a typo in my original mail, it's not a linear regression,
>> but a polynomial regression (since the result was obviously polynomial)
>>
>> cheers
>> c
>>
>>
>> Le 19/10/2016 à 15:06, katja a écrit :
>>>
>>> Changing the thread title to reflect the new approach. Extract of the
>>>
>>> - I suggested using iemlib's hi pass filter recipe to improve
>>> frequency response of [hip~]
>>> - Christof Ressi pointed to formula in
>>> http://www.arpchord.com/pdf/coeffs_first_order_filters_0p1.pdf
>>> - this formula calculates feedback coefficient k = (1 - sin(a)) /
>>> cos(a) where a = 2 * pi * fc / SR
>>> - the filter implementation is y[n] = (x[n] - x[n-1]) * (1 + k) / 2
>>> +   k * y[n-1]
>>> - following convention in d_filter.c (and pd tilde classes in
>>> general), trig functions should best be approximated
>>> - Cyrille provided libre office linear regression result for
>>> (1-sin(x))/cos(x)
>>>
>>> Thanks for the useful infos and discussion. My 'math coach' suggested
>>> using odd powers of -(x-pi/2) in an approximation polynomial for
>>> (1-sin(x))/cos(x). The best accuracy/performance balance I could get
>>> is with this 5th degree polynomial:
>>>
>>> (-(x-pi/2))*0.4908 - (x-pi/2)^3*0.04575 - (x-pi/2)^5*0.00541
>>>
>>> Using this approximation in the filter formula, response at cutoff
>>> frequency is -3 dB with +/-0.06 dB accuracy in the required range 0 <
>>> x < pi. It can be efficiently implemented in C, analogous to an
>>> approximation Miller uses in [bp~]. So that is what I'll try next.
>>>
>>> Attached patch hip~-models.pd illustrates and compares filter recipes
>>> using vanilla objects:
>>>
>>> - current implementation, most efficient, accuracy +/- 3 dB
>>> - implementation with trig functions, least efficient, accuracy +/- 0.01
>>> dB
>>> - implementation with approximation for trig functions, efficient,
>>> accuracy +/- 0.06 dB
>>>
>>> A note on efficiency: coefficients in [hip~] are only recalculated
>>> when cutoff frequency is changed. How important is performance for a
>>> function rarely called? I'm much aware of the motto 'never optimize
>>> early', yet I spent much time on finding a fast approximation, for
>>> several reasons: it's a nice math challenge, instructive for cases
>>> where performance matters more, and I want to respect Miller's code
>>> efficiency when proposing a change. Today pd is even deployed on
>>> embedded devices so the frugal coding approach is still relevant.
>>> After 20 years.
>>>
>>> Katja
>>>
>>>
>>> On Tue, Oct 18, 2016 at 10:28 AM, cyrille henry <ch at chnry.net> wrote:
>>>>
>>>>
>>>>
>>>> Le 18/10/2016 à 00:47, katja a écrit :
>>>>>
>>>>>
>>>>> The filter recipe that Christof pointed to was easy to plug into the C
>>>>> code of [hip~] and works perfectly. But when looking further in
>>>>> d_filter.c I came across an approximation function 'sigbp_qcos()' used
>>>>> in the bandpass filter. It made me realize once more how passionate
>>>>> Miller is about efficiency. I'm not going to make a fool of myself by
>>>>> submitting a 'fix' using two trig functions to calculate a filter
>>>>> coefficient when a simple approximation could do the job. So that is
>>>>> what I'm now looking into, with help of a math friend: an efficient
>>>>> polynomial approximation for (1-sin(x))/cos(x).
>>>>
>>>>
>>>> according to libre office linear regression, for x between 0 and Pi,
>>>> -0.057255x³ + 0.27018x² - 0.9157x + 0.99344
>>>>
>>>> the calc is in attachment, if you want to tune the input source or
>>>> precision.
>>>> cheers
>>>> c
>>>>
>>>>
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