1/f noise basically kills averaging. You collect more signal but at the same time equally more noise.
An Interesting Fourier Transform – 1/f Noise (2007)
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Re: An Interesting Fourier Transform – 1/f Noise (2007)
#12Earlier quoted context omitted.
Pink noise is also perceptually flat noise, because it contains the same energy in each octave (or decade). 'truly' white noise (equal energy for equal bandwidth) tends to sound quite tinny/hissy in comparison.
I went through a phase of using ~whitenoise while working to block out distractions. Actual white noise indeed sounds really bad and grating. The best for me was a mix of pink and brown noise, pink for an ~equal baseline and brown to make it sound a little more mellow. I suspect most/all generators meant to block out noise do something similar. It really sounds pretty bad without that, especially for anything more th…
Yeah. pink noise is often confused with white noise in audio because it looks flat on a lot of equaliser displayers (because they show energy per octave instead of energy per Hz).
Re: An Interesting Fourier Transform – 1/f Noise (2007)
#131/f noise basically kills averaging. You collect more signal but at the same time equally more noise.
Yup, it has the fun property that you'll get the same error in your estimate of the mean regardless of averaging time (though since it's not stationary this isn't even really that well defined).
(though of course, a random walk means you'll get even worse as you measure for longer...)
Re: An Interesting Fourier Transform – 1/f Noise (2007)
#14The comment section at the bottom of the article is pretty interesting. 20 years of people thinking about this.
As noise, its 1/f is 0.748544393 years per comment, haha.
(The frequency is 42.3338481 nanohertz.)
Re: An Interesting Fourier Transform – 1/f Noise (2007)
#15Just as interesting and surprising to me is that this 0-100Hz line is unexplained . Given that signal processing is the foundation of pretty much all digital technology, as well as the analog technologies that came before, I've kind of assumed every segment of a frequency plot be well studied and understood, with half a dozen of names to choose for (doublesine quefrency this, Kowalski-Shannon that...) and a heap of d…
Compounding the mystery is that it crops up everywhere, not just electronic noise plots. But outside of a few systems such as electronic noise in a laboratory setting, it's phenomenally hard to measure. For one thing, to get into the 1/f domain, you have to measure things for a long time. And the noise measurement itself is noisy. And the number of things that you need to control, such as environmental conditions, increases.
So its existence is often largely treated as an empirical rule of thumb rather than having a specific physical cause.
The other thing to note is that the noise plot in a dataset is probably a curve fit.
Re: An Interesting Fourier Transform – 1/f Noise (2007)
#16I think 1/f is the uniform measure for scaling rather than translations. It's to multiplication what the standard uniform measure is for addition.
If you want to be boring you could call it the uniform distribution for log frequency.
Re: An Interesting Fourier Transform – 1/f Noise (2007)
#17When I was learning DSP, I was surprised by the fact that generating pink (1/f) noise, sample by sample, is not mathematically easy at all.
One practical approach is passing white noise (every sample independent random) through a "pinking filter", which is a sum of a bunch of lowpass filters at different frequencies, so that the sum of their cutoff "knees" approximates the frequency curve of pink noise. Another approach is generating in chunks using Fourier transform from a desired shape. Given the ubiquity of 1/f noise, you'd think there would be a simpler and more direct algorithm, but no.
Re: An Interesting Fourier Transform – 1/f Noise (2007)
#181/f noise basically kills averaging. You collect more signal but at the same time equally more noise.
Yup, it has the fun property that you'll get the same error in your estimate of the mean regardless of averaging time (though since it's not stationary this isn't even really that well defined). (though of course, a random walk means you'll get even worse as you measure for longer...)
This makes me think of the Cauchy distribution, a probability distribution whose average follows the distribution itself rather than converging (hence, the distribution has no "mean" despite being symmetric). Is there any connection here, or is that just a coincidental similarity?
Re: An Interesting Fourier Transform – 1/f Noise (2007)
#191/f noise basically kills averaging. You collect more signal but at the same time equally more noise.
1/f noise does not truly kill averaging, observe how for increasing f, the noise spectrum looks "white" locally, but with a decreasing noise power for ever higher frequencies.
the 1/f noise at significant power levels is restricted to the lower and lower frequencies, effectively a slowly varying reference ("0") voltage of the amplifier, measuring ADC ground every other sample effectively recalibrates the offset voltage of the amplifier, think of "correlated double sampling".
Effectively measuring in sequence 0V, signal, 0V, signal, ... moves the signal of interest to a higher frequency band, where the 1/f noise is more tame.
When a cliff blocks the way of a vehicle, we don't say "cliffs kill vehicle travel", insteas we just drive around it...
Re: An Interesting Fourier Transform – 1/f Noise (2007)
#20Side note: Steve Smith is also the author of the excellent https://dspguide.com/