[sdiy] Adding audio channels, to increase S/N

[Magnus Danielson]

From: Glen <mclilith at charter.net>
Subject: [sdiy] Adding audio channels, to increase S/N
Date: Thu, 04 Sep 2003 03:05:04 -0400

Glen,

> Please, help refresh my memory. 
> 
> If the same signal is fed to multiple audio channels, and their outputs are
> later summed, the S/N ratio is higher than if only using a single channel.
> For example, some people would send the same signal to several channels of
> audio tape, in order to increase the S/N ratio of the tape recording. The
> idea being, the signal would reinforce itself when the various copies were
> added back together, but the random background hiss would not directly add
> up, and be somewhat muted in comparison to the signal.
> 
> I just can't remember what the improvement is, measured in dB, when you
> double the number of channels used. Is it 3dB? I know it wasn't much for a
> simple doubling, but if you had several channels available, the improvement
> was supposed to be dramatic.

It is 3 dB for each doubling... if the worst noise is internal to the signal
chain and not in the signal to start with...

> I should remember the answer to this, but my mind must be distracted at the
> moment.

It works like this... if you have signal of strength S and internal noise of
level N, then the output from the sum for the signal is S+S = 2*S since the
two output signals is in phase. For the noise phase is random, with random
phase the two noise variants is orthogonal and the sum output is the vector
sum of two vectors being 90 degrees from each other... this ends up as being
sqrt(N²+N²) = N*sqrt(2) due to Phytagoras... so real signals doubles (+6 dB)
when noise only rises with square root of 2 (+3 dB). When looking at the S/N
this new S'/N' is +6-3 = +3 dB higher than original S/N.

Cheers,
Magnus