Celestia Forums

Hello all,

I'm curious if anyone has any ideas about 1/f noise?

The reason I ask here is that quite a lot our observations of space take it into account yet no-one really understands what it is.

To make it even more confusing I took a fourier transform of a sine wave but instead of a range of 0-2pi I offset it by a small amount, eg 0-2pi+/-0.0001 and behold a 1/f noise spectrum appeared on the frequency domain! This was simulated on a computer so no noise other than rounding error should be present which is far to small to explain the magnitude of the frequency spectrum.

I acknowledge that the frequency domain is reconstructing a non sine wave due to the fact I haven't sampled exactly at the period of the sine wave, my point however is that real life data never can be.

So is 1/f just our own instruments/technology being used beyond their limits? If so, how does this affect the universe as we currently see it?

Any physisists/astronomers/mathematicians out there that can shed some light or an opinion on this topic?

Might help if you (or someone else) explained what 1/f noise is. Is it anything to do with what we might see in Celestia? Or is this just a general (albeit very technical) physics/astronomy question?

You won't directly see it in celestia but the images and data collected to make celestia accurate have this noise embeded in them.
This may sound like a quote from "the matrix" but in this case it's also quite true: it's everywhere you look, everything you see and touch but what it is?. Well almost everything anyway!

Its a general question (yes technical) that relates to many feilds including astronomy, optics, sound, light spectra etc.

In sound it is refered to as pink noise.
In astronomy it is found in stars light outputs etc.
It can be identified relatively easily, it just can't be explained.

In a nutshell, for 1/f noise: the power in noise = 1/ (frequency)
Since the frequency extends to zero this is telling us we approach infinite power as the frequency approaches zero. This raises many issues to say the least!

Engineers accept it and work around it, most mathematicians don't want to know about it and when they do, they get involved in playing with the maths and forgeting the question!

So I figured I'd ask a community that thinks in broad terms regularly; can't get much broader than astronomy and physics!

Hope that helps, however I'm asking the same question as you are: what is it?

mrzee,

From your description, it sounds like you are taking a finite fourier transform of a sine wave from 0 to 2*Pi+c where c is very small. What you have noticed is due to the fact that there is a c0 discontinuity in the effective infinite curve. The finite fourier transform is basically the infinite fourier transform of the infinite curve made by stitching the finite section end-to-end repeatedly from -infinity to +infinity. This effect can be controlled by windowing the finite curve section. By using an window which tapers exponentially at both ends you can insure that the boundary conditions will be continuous across all derivitives which will clean up you signal greatly without losing much of the relevent frequency/phase information. For more information on tailoring the windowing function to your specific application, I would recommend asking an electrical engineer as this is a typical undergrad problem for them.

See also:
http://mathworld.wolfram.com/FourierSeries.html
http://mathworld.wolfram.com/FourierTransform.html
http://mathworld.wolfram.com/GibbsPhenomenon.html
http://mathworld.wolfram.com/DirichletF ... tions.html

I hope that helps,
Walton Comer

Hi Walton,

Thanks for the info it does explain the fourier transform issue as I wrote it. I actually am an electronics engineer so I uderstand what the problem is, I just find it curious that happens to manifests itself as 1/f.

Whilst studying (many many moons ago!) no one understood the mechanisim for it but were happy to accept it was there and work around it (1/f that is). The sine discontinuity example is well known but engineers use as a stop light, once they see it they know they have gone too far with what they are doing an discard the results. They never question its curve for example. It's just a marker for identifying the limits of the job at hand.

Even today researchers look for places to find it, quite successfully too, however they don't seem to wonder why its there in the fisrt place.

To be honest, until recently neither did I. Then the thought occured to me, it's pretty much everywhere in nature when we look for it. Something that affects so many non related feilds but no apparent conection. How is astronomy linked to the human memory for example, both have 1/f noise inbuilt!

So many totally different fields all with one thing in common, 1/f.

Here's a pretty wild theory: 1/f appears with long time constants. The universe is how old? No real accurate answer but its a hell of a lot older than our history by a long shot! Yet we assume our data to be correct on large time scales. How much of this data is likely to be influenced by 1/f, are we deluding ourselves and creating a false impression of the universe we inhabit? It could certainly explain why different reasearchers come up with different results to the same problems.

The longest time constants appear in astronomy, this should also suggest that astronomical data would be the most influenced by it. Scary thought! There may be a possibility that the noise in our measurements is magnitudes larger than what we are measuring. Note this has nothing to do with the accuracy of the instrument itself, rather, the uncertainty of what is being measured itself is in question here. Since our life span is so short compared to the age of the events we are witnessing it would take many generations of accurate data to even realise the level of the noise present in order to extract the true data!

Just my thoughts anyway. Was hoping someone may have some ideas. Or even if my little thread would influence someone's curiosity enough to find the answer I'd be happy.