On 02/05/2017 07:52 PM, robert bristow-johnson wrote:
> 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?
Ah OK - you have a different definition of "envelope" than I do. That's
fine.
> 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.
The Microchip dsPIC processors are about 10-15 years old now. They
generally have about a 40MIPS instruction rate (although some parts are
rated to run faster and you can get away with overclocking them) and
they can do a 16x16->48 MAC in a single cycle with simultaneous operand
fetching and addressing so convolutions can achieve one tap per clock.
They're inexpensive (under $10), have a nice complement of peripherals,
on-chip RAM and Flash memory and the development toolchain is free. Most
of them have on-chip 12-bit ADCs and some even have 16-bit sigma-delta
DACs so it's possible to implement a complete audio processing system
with a single chip (albeit somewhat low SNR).
now, here is the touchy question: care to tell us how you designed the
coefficients for the APF pairs?
I mentioned the general process in an earlier email - started with
Olli's coefficients, interpolated them from 8 poles to 12 and then
optimized with simulated annealing to get improved image rejection.
Eric
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