Summing Noise Sources

There is no absolute "crest factor". Enough samples of white (random) noise eventually conform to a Gaussian distribution, and the probablity of an outlier decrease as you get further away from the mean.

One standard deviation from the mean includes more than half the observations, two standard deviations includes about 95%, and three includes about 99.5%. Do a google search on the Gausian distribution for precise numbers.

Pink noise isn't entirely random - one way of thinking of it is to imagine that the noise is being high-pass filtered by a rather odd filter - so life gets even more complicated, but no in the way you propose.

Noise - even pink noise - doesn't have this kind of regularity.

It might be - if it were true. Find a statistician. CSIRO has a statistical consulting service, but they aren't cheap.

-- Bill Sloman, Nijmegen

See

Crest factor is not defined in terms of time domain amplitude, there is no peak. All the energies, peak, average, whatever, increase by the same ratio, so the crest factor remains the same.

IMO, the apparent anomaly lies in the concept of the CF of a random signal, which, strictly speaking, is infinite for a sufficiently long sample period, because even though the signal is bandlimited, the amplitude probability distribution still has infinitely long tails, at least in theory. The figure of 4 appears to be the result of clipping the tails. When you add a pair of these noise signals, the resulting double-sized peaks are even less probable than the originals.

-- Joe

"Fred Bloggs"

** Why

It has SFA to do with my Q.

( snip FB's manic diatribe of misconceptions - least we have them out of the way now )

........ Phil

"J.A. Legris"

** Completely non relevant.

No matter what the actual, repetitive peak voltages magnitudes seen are - they double when summing two similar, non correlated sources.

While the RMS voltages obey another rule.

So the CF goes up.

...... Phil

What you deserve is lots of *********** thingies and a lot of swearing about what an ignorant autistic moron you are, and why can't you use google?

But in fact, the statistics of summed noise is still noise. If each signal has a finite crest factor (ie, it comes from a real circuit) then the sum has the sum of the crest voltages, as you note. If the signals are truly gaussian, each has an infinite crest factor, so their sum has an infinte cf too.

Gaussian noise has an unlimited p-p swing, if you're willing to wait long enough. Visually, p-p/RMS runs about 5:1 in most situations. If each signal looks like that, their sum will, too.

Your apparent paradox is resolved by the observation that adding your signals does seem to double the peak voltage, but it also severely reduces the probability of the peaks adding up.

pbbbbtttt!

John

An opamp is usually specified by the current and voltage noise referred to the input. It seems logical that there should be at least some correlation between those noise sources. So the total noise should be somewhere in between the sum and the RMS sum. What do you think?

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

"John Larkin"

** But indeed they must - so the CF goes up ( in general) with summed, real noise sources.

Google is a bit quiet on this one.

Must be a * source * of some embarrassment.

Intriguing - but.

...... Phil

"Vladimir Vassilevsky"

** Oooooh - now * that * is profound.

The twain have always been treated as independent noise sources in texts I have seen.

Naughty ......

....... Phil

Yes, if they are positively correllated the RMS sum will be higher than if they aren't. But Phil seemed to specify random noise, which I took to be uncorrelated.

Which brings up the point: in an opamp or more generally a transistor, are current and voltage noises significantly correlated? I'm guessing they aren't.

John

Look at it another way. When you average two random noise sources the variance goes down, but the tails of the amplitude distribution are still there, albeit somewhat thinner. If you calculate the CF between the same upper and lower limits of the distribution as you chose for the unavaraged data, it will seem to increase, but if you scale the limits to match the decreased variance you'll get the same value. It all depends on where you set those limits, so it's not anomalous, it's statistics.

-- Joe

But "crest factor" for noise is mostly an illusion. It depends on how long you are willing to wait and/or how lucky you are.

Look at some wideband noise on a digital scope. Turn on infinite persistance, so you see all the peaks. The band of accumulated peaks grows with time, slower and slower, but grows without limit. There *is no* crest factor for gaussian noise, unless you accept "infinity."

If you have two identical sources of gaussian noise, say 1 volt RMS each, and observe them with any possible instrument, they of course look the same. Now sum them and scale down by 0.7071; the scaled sum will be indistinguishable from the previous observations.

If the noise is clipped, so the signals have finite peak voltages, then of course the summed signal has the summed peak voltages, just like a music signal or such. But you may have to wait a very long time for the peaks to gang up.

John

And if the signals are gaussian noise, the crest factor goes from infinite to twice infinite.

John

"John Larkin"

** Anyone for a game of sophistry ?

Best two out of three ??

....... Phil

Sorry, mathematics is mathematics. Using the words "crest factor" has no influence on how the universe behaves.

Also google "central limit theorem."

John

YOU GROPING COCKSUCKING POMMY CUNT!!!!!

IT'S FUCKING HIGH SCHOOL STATS!!!!!!!

*****FOAD!!!!!!*****

(Oops - lost my temper (blush) BTW, what does "pommy" mean?)

Phil. let me suggest looking at it this way. As you know, when you look at noise with an analog CRT oscilloscope, as you increase the intensity control, more and more small (and rare) signal peaks come into view. Looking at this it's clear how the crest factor is not clearly defined on the CRT screen. However you define it there are some peaks above the so-called crest level, which you can see if your intensity control is turned high enough, and if the CRT writing speed is fast enough, and if you wait long enough. So statistically speaking, some fraction, say 98%, will be below your crest-level definition, and 2% will be above.

Now you add in a second identical-amplitude noise signal, with its own small fraction of peaks above the crest level. We know the RMS level will go up by square-root-2 and as it happens, we also know the crest level will go up by sqrt-2. The reason the crests don't add up to 2x as you surmised is that since the peaks that exceed the old crest level arrive rarely, the chance of it happening simultaneously with the two independent noise sources is very rare indeed. Of course it does happen, but those events are lumped in with the 2% of the time the combined signal rises above the new 1.4x higher crest level.

That's what statistics tell us and that's what we observe.

I'm pleased to attempt to do that for him. Damn! You're an ass.

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. 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. On the other hand you might just come up with some arbitrary equation that you pulled out of your arse and then swear at anyone who does not agree with you.

Chris