Heyho,
I just wanted to ask if anyone has made some experiences with the [hilbert~]-object?!
Especially does anyone know how 'good' that thing (ehh Mr. Hilbert~) is?? I tried to use it with other signals than the bell-sound but with relatively poor results...
...and where are the allpassS "coeffs" coming from??
...will one get better results with a higher order??...and how to calculate that...

..hmm..
Bye,
Flipp

[hilbert~] works fine from ~80 Hz till ~Nyquist/2.

Olli Niemitalou has published coefficients for a fine quadrature transformer which works from ~20 Hz up till ~Nyquist.

http://yehar.com/blog/

Olli's filter can be implemented in Pd, using 8 [biquad] objects and 1 [delay~]. With pd-extended installed, you can see how it's done in attached patch. If you want to be entertained with plots and graphs on allpass filtering and quadrature transform, see this:

http://www.katjaas.nl/hilbert/hilbert.html

Katja

http://www.pdpatchrepo.info/hurleur/hilbert-compare.pd

Hey Katja,
first of all thank you for pointing out to me that there is an object to plot stuff like lissajous-curves (at least it seems to be at first glance..). ...I already thought of building something like that with pd's datastructures... personally I don't like them much, so I never started..

..of course I already stumbled over your pages "decades" ago What can I say: Really entertaining and nice to read (..a good contrast..) .

Concerning the above problem: No problem, I just thought of a frequency-multiplication instead of a -addition (per partial!!) at first and it just didn't sound like a multiplication...
Is the only reason for analytic signals in general the complex math?!
..I wonder if there are also "hyper-analytic" signals utilising quaternions..

I thought of a nice application for a hilbert transform: change the beating characteristic of detuned oscillators. Two detuned square waves will cancel completely when out of phase, while two saw waves won't (unless one is inverted). In both cases all harmonics will reinforce when they're in phase. You can change this with two [hilbert~] objects (or one if you modify it to have two inlets). It's an easy way to make a variant of any waveform.

@Flipp said:

I just thought of a frequency-multiplication instead of a -addition (per partial!!) at first and it just didn't sound like a multiplication...

It is possible to multiply frequencies per partial if you manage to isolate them sufficiently. Instead of direct complex multiplication, you need to do complex division and compute instantaneous amplitudes and frequencies (analysis), multiply the frequencies, and recreate the signal (resynthesis). See attached patch for a demo. Real world signal tend to have so many partials however, that the method is impractical.

@Flipp said:

..I wonder if there are also "hyper-analytic" signals utilising quaternions..

It seems that quaternionic and other hypercomplex signals are mostly used in image processing and other 2D / 3D processing. How could one create more than two orthogonal phases out of a 1 dimensional (audio) signal? And, if possible at all, what information could one derive from the extra phases? Intriguing matter...

By the way, analytic signals are normally not considered very useful in audio processing either, except for single sideband modulation in radio transmission. Yet I use analytic signals in my Pd setups for a lot of purposes. For example, to find amplitudes for an ultra fast compressor / expander ([qompander~], shared on this forum).

Katja

http://www.pdpatchrepo.info/hurleur/freq-multiplier.pd