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

[Czech Martin]

Correlated signals add arithmetically, uncorrelated
geometrically.

N pathes thus give N times amplitude for your signal
but only SQRT(N) times noise.

S/N is then improved by N/SQRT(N)=SQRT(N) or 
20*log10(SQRT(N))=10*log10(N) if you like dB bettter.
The S/N will increase only by 3dB if N is doubled.

N   S/N dB
2    3
4    6
8    9
16   12

The increase is really slow.

The assumption was that the noise is totally uncorrelated
in all channels (not true in reality) and that
the signal is totally correlated (maybe also not true).

The principle is sometimes used to get the outmost S/N
in amplifiers (several parallel input stages).
Of course this only works, if the resulting low
input impedance is desired.

m.c.

> -----Original Message-----
> From: Glen [mailto:mclilith at charter.net]
> Sent: Donnerstag, 4. September 2003 09:05
> To: synth-diy at dropmix.xs4all.nl
> Subject: [sdiy] Adding audio channels, to increase S/N
> 
> 
> 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.
> 
> I should remember the answer to this, but my mind must be 
> distracted at the
> moment.
> 
> Thanks for any info,
> Glen Berry
> 
>