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January 04, 2011


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George Storm

I'm clearly missing something here, as I can't see any reason that there should be any relation between the triangular waveform and the topic under discussion. You could argue with equal justification a similar relationship with the peaks of a waveform that consisted of two equal sinusoids - and this would give you a lower-bound factor of two.
The old-boys' physiologically-based oscilloscope method for Johnson noise (turning the level of an oscilloscope up so the trace looked bright, and estimating the RMS as 2/7 of the apparent peak level on the oscilloscope) was remarkably accurate. That would make 1/sqrt(3) an upper bound - but one that was a factor of two above the actual value - and so not generally very useful.
And if we are talking about measuring interference rather than random noise, the RMS can actually be larger than 1/sqrt(3) times the peak.

George Storm

Erratum: "lower bound" should of course read "upper bound"

Peter Kay

In the audio world I have always used
White RMS noise = (peak to peak)/6.
Pink RMS noise = (peak to peak)/4
Your measurement is indicate noise is closer to (P-P)/3

John D.

The key to this estimate is that the probability distribution function is flat over the range of the variable. This is true for any sawtooth or triangular waveform and is also true for a random waveform when they all share the same range as shown here.

The white RMS and pink RMS are both smaller than the upper bound which is precisely the point.

The graphics shown came from some code in GWBASIC. If anyone would like to have it, I'll gladly send it along. Just e-mail me at ambertec@ieee.org and I'll reply.

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