Re: [LAU] Subject: Albums under a label recorded and/or mixed with Linux

On Sun, Sep 26, 2010 at 4:12 AM, <fons@email-addr-hidden> wrote:
> The reason is that step (5), multiplication in the
> frequency domain, is equivalent to convolution in the
> time domain. And the convolution of two signals of N
> samples (T1 and T2) has lenght 2*N-1. This means that
> this result is wrapped around in step (6) since the
> inverse FFT produces only N samples.

Doesn't this also apply to basic digital "mixing" of audio signals --
and appears to be the fundamental difference in both sound and
algorithm between "analog summing bus", where each digital output in
the mix is sent to an independent DAC, getting full 24 bit resolution
per and full samplerate per signal, and then summing that in the
analog domain. This effectively multiplies the bitrates of all the
sources and is the equivalent to the "convolution of C-number of
signals of N samples (T1 and T2) has length C*N-1"

And yet, traditional digital mixing, would mix C-number of signals of
N samples each into N samples. Which is a vastly different quantity of
information than would be conveyed via an analog summing bus which
would be C*N samples.

When is it valid, and not valid, for so much information to disappear
in the process of performing an analog-domain task in the digital
realm?

In fact, both sampling and mixing are both "multiplication in time"
operations, -- per
http://www.analog.com/static/imported-files/application_notes/5847948184484445938457260443675626756108420567021238941550065879349464383423509029308534504114752208671024345AN_756_0.pdf
///// ///// ///// ///// ///// /////
"As stated previously, the sampling process is a multi-
plication process in time and, therefore, a convolution
process in the frequency domain. While it is clear that a
mixer multiplies two analog signals in the time domain
with the results being the convolution of these two in the
frequency domain, it may be less clear that the sampling
process is also a multiplication in time process."
///// ///// ///// ///// ///// /////

There's also no reason why a digital equivalent of an analog summing
bus -- which preserves or allows direct control over, and optimization
of both bit-depth preservation, and also sample-rate multiplication,
on a per-source basis. This would allow the sound engineer to
design-in the desired tradeoffs in resulting sound, sample-rate, bit
depth, etc -- on a per-signal basis. Since it doesn't make sense to
give the exact same treatment to synthesized atmosperics layered on
top of multi-miked results (where you might want to put a premium on
the phase-relationships between microphones, while preserving bit
depths would just pickup noise with higher fidelity).

Perhaps, products like the following appear to be heading in that
direction: http://www.slatedigital.com/vcc.php ... and of course this
is a long contentious topic (
http://emusician.com/mag/emusic_sum_tracks/ ), which IMHO is clarified
by considering a convolution and information-theoretic-perspective to
the problem of mixing signals in a digital system ....

-- Niels
http://nielsmayer.com
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Received on Mon Sep 27 00:15:01 2010