Re: Summing Noise Sources

On Tue, 2 Oct 2007 12:53:12 +1000, "Phil Allison"
<philallison@xxxxxxxxxx> wrote:


"Chris Jones" <lugnut808@xxxxxxxxxxxxxxxx> wrote in message
news:13g2ofrbl9ctg6c@xxxxxxxxxxxxxxxxxxxxx
Phil Allison wrote:


** Hi all,

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 circa 4 times
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 doubled 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.

So, summing noise sources INCREASES the Crest Factor .

Is not anomalous ??



If your noise sources are Gaussian, then the peak value could be
arbitrarily
large if you wait long enough and so there is no meaningful crest factor,
as many people have explained to you.


** I never mentioned Gaussian - only real noise sources that have finite
amplitude limits.

Whatever approximation method of assigning a peak amplitude one adopts -
that number will double when two similar (equal RMS value) noise sources are
summed.


If on the other hand, the noise
sources are not Gaussian, then provided the voltages are truly
uncorrelated
at any given point in time, you should be able to calculate the new crest
factor by convolving the probability density functions.


** So you too agree that CF increases when un-correlated noise sources are
summed.


NOBODY here seems to agree with you.

John

.

Relevant Pages

  • Re: Summing Noise Sources
    ... If we have two or more random noise sources (be they pink, ... the square root of that sum. ... Sounds like a confused school boy mindlessly regurgitating some rules with no rhyme or reason...Your so-called RMS is a simple standard deviation of two independent random variates, and as anyone knows, the standard deviation of the sum is the RSS of the component deviations. ... There is no peak value for the idealized amplitude statistics, there may be a practical limitation in the real world, but the idealized model usually fits with less than 1e-24 chance of deviation from reality, that's why people consider it useful. ...
    (sci.electronics.design)
  • Re: Summing Noise Sources
    ... If we have two or more random noise sources (be they pink, ... the square root of that sum. ... Any steady noise source will have a "peak to average ratio" or Crest ...
    (sci.electronics.design)
  • Re: Summing Noise Sources
    ... If we have two or more random noise sources 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. ... Any steady noise source will have a "peak to average ratio" or Crest Factor - which is the number ratio of the magnitude of the peak value to the steady RMS voltage level. ...
    (rec.audio.tubes)
  • Re: Summing Noise Sources
    ... If we have two or more random noise sources (be they pink, ... the square root of that sum. ... Any steady noise source will have a "peak to average ratio" or Crest ...
    (sci.electronics.design)
  • Re: Summing Noise Sources
    ... taking the square root of that sum. ... The latter gives a total RMS noise voltage while the former gives the ... Any steady noise source will have a "peak to average ratio" or Crest ... But if you sum two pink noise sources of the same average amplitude, ...
    (sci.electronics.design)