Interpreting noise

Started by February 23, 2006
How do I know the difference between a signal which is decreasing in
power as frequency increases because of its characteristic distribution
(e.g., pink noise, brown noise), and a signal which is decreasing in
power as frequency increases because it's band limited (e.g., white
noise with a continuous falloff)?
Thanks,

Trevor

goodchild.trevor@gmail.com wrote:
> How do I know the difference between a signal which is decreasing in > power as frequency increases because of its characteristic distribution > (e.g., pink noise, brown noise), and a signal which is decreasing in > power as frequency increases because it's band limited (e.g., white > noise with a continuous falloff)? > Thanks, > > Trevor >
Brown noise? That's a new one. If you take white noise and shape it with a 3dB/octave roll-off filter then it'll be pink noise. If it's falling off at 6dB/octave then it's a more 'normal' bandlimited process. Assuming (nice word, that) that you can get good data and a good spectrum, look at the slope of the rolloff. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/
Tim Wescott said the following on 23/02/2006 20:13:
> goodchild.trevor@gmail.com wrote: >> How do I know the difference between a signal which is decreasing in >> power as frequency increases because of its characteristic distribution >> (e.g., pink noise, brown noise), and a signal which is decreasing in >> power as frequency increases because it's band limited (e.g., white >> noise with a continuous falloff)? >> > Brown noise? That's a new one.
Brown noise = Brownian noise, i.e. 1/f^2 spectrum, or 20 dB/dec, or 6 dB/oct. In answer to the OP's question, I don't think there's a lot you can do to identify the difference. Whether the spectral response of the received signal is due to band-limiting or due to the inherent noise process, they're exactly equivalent. Pink and brown noise can be created by low-pass-filtering white noise appropriately, which is exactly equivalent to (appropriate) band-limiting. -- Oli
Oli Filth wrote:
> Tim Wescott said the following on 23/02/2006 20:13: > > goodchild.trevor@gmail.com wrote: > >> How do I know the difference between a signal which is decreasing in > >> power as frequency increases because of its characteristic distribution > >> (e.g., pink noise, brown noise), and a signal which is decreasing in > >> power as frequency increases because it's band limited (e.g., white > >> noise with a continuous falloff)? > >> > > Brown noise? That's a new one. > > Brown noise = Brownian noise, i.e. 1/f^2 spectrum, or 20 dB/dec, or 6 > dB/oct. > > > In answer to the OP's question, I don't think there's a lot you can do > to identify the difference. Whether the spectral response of the > received signal is due to band-limiting or due to the inherent noise > process, they're exactly equivalent. Pink and brown noise can be > created by low-pass-filtering white noise appropriately, which is > exactly equivalent to (appropriate) band-limiting. > > > -- > Oli
I wonder if a histogram would offer a clue. Is it true that if noise has the same PSD, that it also has the same PDF? It has just been too long since college for me to remember this stuff. John
Tim Wescott wrote:

> Brown noise? That's a new one.
Brown noise follows the statistics of a random walk (Think Brownian motion). 1/f^2 Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
john wrote:

> Oli Filth wrote: > >>Tim Wescott said the following on 23/02/2006 20:13: >> >>>goodchild.trevor@gmail.com wrote: >>> >>>>How do I know the difference between a signal which is decreasing in >>>>power as frequency increases because of its characteristic distribution >>>>(e.g., pink noise, brown noise), and a signal which is decreasing in >>>>power as frequency increases because it's band limited (e.g., white >>>>noise with a continuous falloff)? >>>> >>> >>>Brown noise? That's a new one. >> >>Brown noise = Brownian noise, i.e. 1/f^2 spectrum, or 20 dB/dec, or 6 >>dB/oct. >> >> >>In answer to the OP's question, I don't think there's a lot you can do >>to identify the difference. Whether the spectral response of the >>received signal is due to band-limiting or due to the inherent noise >>process, they're exactly equivalent. Pink and brown noise can be >>created by low-pass-filtering white noise appropriately, which is >>exactly equivalent to (appropriate) band-limiting. >> >> >>-- >>Oli > > > I wonder if a histogram would offer a clue. Is it true that if noise > has the same PSD, that it also has the same PDF? It has just been too > long since college for me to remember this stuff. > > John >
Nope, although most noise process tend toward Gaussian with averaging. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/
Jerry Avins wrote:
> Tim Wescott wrote: > > > Brown noise? That's a new one. > > Brown noise follows the statistics of a random walk (Think Brownian > motion). 1/f^2
sometimes it's called "Red noise". http://en.wikipedia.org/wiki/Colors_of_noise personally, i think "red noise" is less scatolgical and positions pink noise nicely as halfway between red and white noise. if the -3 db/oct were called "ochre noise" or "tan noise", then "brown noise" would be appropriate for -6 dB/oct. r b-j
robert bristow-johnson wrote:
> Jerry Avins wrote: > >>Tim Wescott wrote: >> >> >>>Brown noise? That's a new one. >> >>Brown noise follows the statistics of a random walk (Think Brownian >>motion). 1/f^2 > > > sometimes it's called "Red noise". > > http://en.wikipedia.org/wiki/Colors_of_noise > > personally, i think "red noise" is less scatolgical and positions pink > noise nicely as halfway between red and white noise. if the -3 db/oct > were called "ochre noise" or "tan noise", then "brown noise" would be > appropriate for -6 dB/oct.
Brown noise is not named after a color. It is named in honor of a person (whose name happens to be Brown). http://en.wikipedia.org/wiki/Brownian_motion Strangers meet and introduce themselves. The first says that he has a very hard name; the second says that he's sure his name is harder. The first is sure he takes the cake: "My name is Stone. Not much harder than that." The second says, "Whatever your name may be, my name is Harder." Odd things happen when words become names. Apropos brown: on the UPS website: "UPS, the UPS brandmark and the color brown are registered trademarks of United Parcel Service of America, Inc. All rights reserved." Software patents are tame by comparison. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Jerry Avins wrote:

> Odd things happen when words become names. Apropos brown: on the > UPS website: "UPS, the UPS brandmark and the color brown are > registered trademarks of United Parcel Service of America, Inc. > All rights reserved." Software patents are tame by comparison.
The German Telekom tried to have the CMYK Magenta characteristic for their ads protected some time ago but were denied, as far as I know. Martin -- Quidquid latine scriptum sit, altum viditur.
Thanks for all the help guys - my intuition was that the two were
indistinguishable, but I don't have a lot of experience in this area.

-Trevor