Re: Summing Noise Sources

Phil Allison wrote [snip to below]

Is anomalous - no ??

Probably not.

If you add a sample of pink noise to a copy of itself, then
the peak value will double. That is because of the 100%
correlation between the two.

If you add two unrelated samples of pink noise, then the
chance of two peaks occurring at the same time is relatively
small...a similar probability to anything else. That is one
possible source of misunderstanding.

So you might expect results ranging between the two values
you give, depending on the degree of correlation. Since you
assume no correlation, the smaller of your values applies.

Also remember to think in terms of samples, rather than
populations. The peak voltage is a measure of probability,
obtained by sampling. If you looked at the population as a
whole, you might expect to see that the sum peak would be
double the peak of the two contributing populations, because
somewhere in that sum population of possible outcomes, there
would *certainly* be your coincidence of peaks. Not so in
samples.

I am absolutely definitely not an expert on probability or
noise.

"Phil Allison" <philallison@xxxxxxxxxx> wrote in message
news:5mb66dFcle75U1@xxxxxxxxxxxxxxxxxxxxx

** Hi all,

Following on from the " Familiar formula ? " thread:

If we have two or more random ( band limited) noise
sources ( be they pink, white or whatever ) and we sum
them, then the TOTAL noise is found by either summing the
individual power levels OR by taking the RMS voltage of
each noise source, squaring the values, summing the
results and then taking the square root of that sum.

The latter gives a total RMS noise voltage while the
former gives the total noise power.

OK ??

But what about the peak value ?????

Any steady noise source will have a "peak to average
ratio" or Crest Factor ( CF) - which is the number
ratio of the magnitude of the peak value to the steady RMS
voltage level.

The CF for band limited pink noise is often quoted as
being about 4 or 12 dB.

But if you sum two pink noise sources of the same average
amplitude, the peak voltage value should double. I say
this because there will be regular points in time when
BOTH noise sources attain maximum ( or near maximum)
values and have the same sign.

So, for the sum, the average power is double but the peak
power is four times that of a single source.

Sounds like the CF of the sum has increased by a factor of
sq rt 2 - ie from 4 to 5.65.

With more independent sources it gets even worse.





....... Phil





.

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