# 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

```
```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.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```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

```
```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.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```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.

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

```