I just did an experiment in Kyma where I took my 10-band EQ made up of cascaded 4th order Butterworth BPF sections. At the output of each frequency band I placed a
PeakDetector? and a
VisualDisplay? readout so that I could examine the variation, if any, of the average peak reading versus frequency band.
This is not a simple problem to solve theoretically, at least not yet for me... But I got a very interesting result...
When I feed in white noise the outputs show a gradual increase of about 2.5-2.7 dB/octave. That tells me that there is a relationship between bandwidth and the expected maximum excursions in a noise signal.
Next, I fed in Pink noise and lo and behold... all of the readouts show a nearly identical value (close enough in astronomical terms).
[ to be more precise... I take all the outputs of those peak detectors and feed into Visual Displays where I then take 20 * Log10 of those inputs. So I'm looking at dB "power" out of those peak detectors. That "power" (quotes because it is pseudo power), is what is constant with frequency when fed by octave spaced, octave wide, filters. So to be precise, the output amplitudes grow as Sqrt[F], while the input true power coming from the filters decreases as 1/Sqrt[F]. Hence the final output with Pink noise remains constant.]
So the interesting thing to me, is that one can reasonably expect to use a Peak Detector as a Power Detector!! When feeding 1/F (Pink) noise into a bank of octave wide filters spaced at octave spacings, you should expect pretty much the same energy contained in the output of each filter of the filterbank. That 1/F refers to power content in the noise, not amplitude. In amplitude units they decay as 1/Sqrt[F].
I'm sure some statistician can point out the obvious connections here, but it was an interesting discovery for me... As it turns out, what I often need is an estimate of the spectral power in each filter band, not its peak excursions. But since a Peak Detector is a funny kind of lowpass filter, it effectively turns into a power detector when used in this way.
I find that very interesting! Don't you?
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DavidMcClain - 24 Feb 2004
