[PD] A 6th order hilbert transformer?

[katja]

The phase shift test from my previous mail expresses quadrature
transformer output as normalized instantaneous frequencies (cycles).
Depending on frequency (within the working range), deviation can be up
to 1/100 of a cycle both for [olli~] and Pd's [hilbert~]. Of those
two, [hilbert~] may even be most accurate, but [olli~]'s working range
extends two octaves lower.

The question is what accuracy and range you need per application, and
how audible deviations are in practice. Would be nice to have a
catalog of quadrature transformers (in Pd abstraction) for testing and
prototyping, including Csound's.

Katja

On Fri, Jun 24, 2016 at 3:47 AM, Alexandre Torres Porres
<porres at gmail.com> wrote:
> I guess I have to find a way to implement it and test it.
>
> By the way, I'm testing max's hilbert~ with olli's - find picture attached.
>
> is this a good way to test it by the way? Seems Max's is more accurate
>
>
>
> 2016-06-23 22:40 GMT-03:00 Matt Barber <brbrofsvl at gmail.com>:
>>
>> Not sure. I've used csound's a lot in ambisonic decoding and it's always
>> worked well.
>>
>> On Thu, Jun 23, 2016 at 6:06 PM, Alexandre Torres Porres
>> <porres at gmail.com> wrote:
>>>
>>> olli's seems easier for me to code, and better than csound's huh?
>>>
>>> thanks
>>>
>>> 2016-06-23 11:27 GMT-03:00 Matt Barber <brbrofsvl at gmail.com>:
>>>>
>>>> csound's hilbert transform is also 6th-order. Code here:
>>>>
>>>>
>>>> https://github.com/csound/csound/blob/2ec0073f4bb55253018689a19dd88a432ea6da46/Opcodes/ugsc.c
>>>>
>>>> On Thu, Jun 23, 2016 at 9:16 AM, katja <katjavetter at gmail.com> wrote:
>>>>>
>>>>> Attached is a zip with test patch for [olli~] and [hilbert~] so you
>>>>> can compare and also check with different sample rates. It seems that
>>>>> Olli's coefficients are optimized to work well from 20 Hz up at 44K1
>>>>> sample rate, and Pd's built-in from 80 Hz up. They both work at other
>>>>> samples rates too, but with different range.
>>>>>
>>>>> Since the coefficients for x[n-2] and y[n-2] are non-zero in the
>>>>> biquads, the maximum phase shift  is as large as in any 2nd order
>>>>> section, therefore I think the four sections together are 8 order
>>>>> equivalent indeed.
>>>>>
>>>>> By the way, the abstraction in my first response wasn't completely
>>>>> vanilla-compatible, this is fixed in current attachment (for anyone
>>>>> else interested).
>>>>>
>>>>> Katja
>>>>>
>>>>> On Thu, Jun 23, 2016 at 6:24 AM, Alexandre Torres Porres
>>>>> <porres at gmail.com> wrote:
>>>>> > Awesome, I can code it based on that :) but which order is it?
>>>>> >
>>>>> > I see it has 4 biquads, but it doesnt look like an 8th order because
>>>>> > some
>>>>> > coefficients are zeroed out, so I'm confused.
>>>>> >
>>>>> > Another question, does it work at any sample rate? This question is
>>>>> > also
>>>>> > aimed to pd's hilbert~ abstraction by the way.
>>>>> >
>>>>> > cheers
>>>>> >
>>>>> > 2016-06-22 17:27 GMT-03:00 katja <katjavetter at gmail.com>:
>>>>> >>
>>>>> >> Hi, Olli Niemitalou has coefficients published for a higher order
>>>>> >> 'hilbert transformer' on http://yehar.com/blog/, attached is [olli~]
>>>>> >> abstraction based on it.
>>>>> >>
>>>>> >> Katja
>>>>> >>
>>>>> >> On Wed, Jun 22, 2016 at 4:37 AM, Alexandre Torres Porres
>>>>> >> <porres at gmail.com> wrote:
>>>>> >> > Howdy, I'm working on a frequency shifter object (via single
>>>>> >> > sideband
>>>>> >> > modulation / complex modulation).
>>>>> >> >
>>>>> >> > In Max they have a so called "6th order hilbert transformer with a
>>>>> >> > minimum
>>>>> >> > of error". In Pd, the hilbert~ abstraction is 4th order. I'm
>>>>> >> > copying the
>>>>> >> > pd
>>>>> >> > abstraction for now, but I was hoping to use such a higher order
>>>>> >> > filter
>>>>> >> > and
>>>>> >> > also use- but I can't find a source for such a formula. Any help
>>>>> >> > finding
>>>>> >> > it?
>>>>> >> >
>>>>> >> > thanks
>>>>> >> >
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>>>>> >
>>>>>
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>>>>
>>>
>>
>