---------------------------- Original Message ----------------------------
Subject: Re: [music-dsp] � 45� Hilbert transformer using pair of IIR APFs
From: "Eric Brombaugh" <ebrombau...@cox.net>
Date: Sun, February 5, 2017 8:22 pm
To: "A discussion list for music-related DSP" <music-dsp@music.columbia.edu>
--------------------------------------------------------------------------
>
> On Feb 5, 2017, at 12:54 PM, robert bristow-johnson wrote:
>
>> using the analytic filter to get the instantaneous amplitude envelope (and,
>> also, instantaneous frequency by differentiating phase) is something that
>> works only with single sinusoids that are AM'd or FM'd. for music, i think i
>> would LPF the square of the signal (or run an efficient sliding
max algorithm, we discussed this a while back) and work with that.
>
> I'm curious what aspects of a music make the complex magnitude of the
> analytic signal inappropriate for estimating the envelope? In communications
> signal processing we use this often, even for signals that are fairly
> wide-band with respect to the sample rate and it seems to work.
>
well, with a single sinusoid, there should be no intermodulation product so the
analytic envelope should be exactly correct. �but consider:
�
� � x(t) �= �g1(t) cos(w1 t) �+ g2(t) cos(w2 t)
which has for it's Hilbert
� �
y(t) �= �g1(t) sin(w1 t) �+ g2(t) sin(w2 t)
�
and analytic signal
�
� � a(t) �= �x(t) + j y(t)
� � a(t) �= �g1(t) cos(w1 t) �+ g2(t) cos(w2 t) + j( g1(t) sin(w1 t) �+ g2(t)
sin(w2 t) )
� � |a(t)|^2 �= �|g1(t)|^2 �+ �|g2(t)|^2 �+ �2 g1(t)
g2(t) cos( (w1-w2) t )
�
the last term on the right needs to be sorta filtered
out with a LPF to get the correct square of envelope, no?
�
my feeling is that if we're gonna have to put up with
the vagaries (delay, etc) of a LPF anyway, better to just square and filter the
signal.
�
and i dunno what sorta mess this becomes if you had two
sinusoids and were using the analytic signal to derive the instantaneous
frequency.
>> but the reason i am most interested is in a frequency shifter. like the ham
>> radio single-sideband (SSB) thingie. this is not a pitch shifter and detunes
>> harmonic overtones into the inharmonic. but it is totally glitch-free and
>> can sometimes be handy to detune something slightly so that
there is not a buildup of energy at a specific frequency (when there is
feedback of some sort). pitch shifters can do that too, but time-domain pitch
shifters might have glitches for non-monotonic input and frequency-domain pitch
shifters have a huge throughput delay. also, this glitch-free
frequency shifting can be slowly modulated. might be useful for chorusing.
combined with a pitch shifter and pitch detector, you can shift harmonics
without shifting the fundamental (i.e. pitch it up with a pitch shifter and
then bring back down the fundamental to the original pitch.)
>
> Yes - the Bode-style frequency shifter is a fun and useful effect. I've done
> several of them for modular synthesizers using these IIR all-pass structures:
>
> With a dsPIC - http://www.modcan.com/bmodules/dualfs.html
>
> With an STM32F303 - http://modcan.com/emodules/dualfreqshifter.html
>
> Also with a dsPIC - http://synthtech.com/eurorack/E560/
>
> There are example soundfiles at the above sites showing some of the subtle
> and radical variations that are possible with different amounts of shift,
> feedback and various shifting waveforms.
>
kewl. �what kinda number crunching can a dsPIC do? �i know what a PIC is. �so,
how wide is the word and how many MIPS can a dsPIC do? �i guess it's time for
me to google search it.
now, here is the touchy question: care to tell us how you designed the
coefficients for the APF pairs?
--
r b-j � � � � � � � � �r...@audioimagination.com
"Imagination is more important than knowledge."
�
_______________________________________________
dupswapdrop: music-dsp mailing list
music-dsp@music.columbia.edu
https://lists.columbia.edu/mailman/listinfo/music-dsp
