Re: [Faudiostream-users] Hilbert filter

[Oleg N. <ol...@re...>]

On 06/22, Julius Smith wrote:
>
> Maybe clearer now?  See latest filter.lib.

Thanks, the new doc matches my understanding ;)

> I presently vote against a scaling by 2, but I am open to arguments.
> Right now, pospass simply passes only positive frequencies, and
> hilbert is the imaginary part of pospass.  To me this is the simplest
> view.

Agreed, but I was talking about fi.hilbert. Ideally it should turn cos()
into sin(), at least according to its name/documentation, not into sin/2.

> None of these filters is ideal.  By considering lowpass, pospass,
> hilbert, etc., in Faust, you are considering practical filters,
> nothing ideal.

Of course. But as for fi.hilbert, I simply can't imagine any practical
usage of it...


And in fact there was another reason why I was confused. I interpreted
your email as if the new fi.ssbf is always "better" than

	hilbert = _ <: H(a1)', H(a2) with {
		a1 = 0.6923878, 0.9360654322959, 0.9882295226860 , 0.9987488452737;
		a2 = 0.4021921162426, 0.8561710882420, 0.9722909545651, 0.9952884791278;
		H_sect(a) = f ~ _ with { f(y, x) = a^2 * (x + y') - x''; };
		H(as) = seq(i, outputs(as), H_sect(ba.take(i+1, as)));
	};

I showed to Dario, at least for frequency shifting. AFAICS, this is not
necessarily true, this depends. Consider the naive implementations,

	freq_shift_yehar(f) = hilbert  : *(os.oscrc(f)) - *(os.oscrs(f));

and

	freq_shift_ssbf(f) = fi.ssbf(8) : *(os.oscrc(f)) - *(os.oscrs(f));

iiuc the first one will work "better" unless the input frequency is "close"
to SR/4.

Right?

Oleg.