On Thu, 05 Feb 2009 10:28:44 -0600, BreadPaPa wrote:
> Hi, all,
>
> I would like to generate a white noise whose power spectral density is
> 1( flat over all frequency). I used Matlab function wgn to get it:
> wn=wgn(1,10000,1,'linear');
> Does the function above generate a white gaussian noise whose PSD is 1?
>
> Then I did simple experiment to check its PSD. I used Matlab function
> periodogram without any window:
> [p,w]=periodogram(wn);
> figure; plot(w,p);
> Theoretically, the PSD of a white noise should be flat( or at least flat
> looking in numerical computation). But the plot showed the PSD of wn is
> totally noisy, no flat looking at all. So I got confused about that.
>
> Could you guys check if I made mistake here? Can you figure a way to
> generate white noise whose PSD is 1 in Matlab? Thanks a lot!
>
> Steve
(sigh).
Study stochastic processes until you understand the difference between an
expectation value of a process, and the value of one sample of the
process.
Then come back and ask your question again, if you still think it makes
sense.
--
http://www.wescottdesign.com
Reply by HardySpicer●February 5, 20092009-02-05
On Feb 6, 5:28�am, "BreadPaPa" <iamstevew...@yahoo.com> wrote:
> Hi, all,
>
> I would like to generate a white noise whose power spectral density is 1(
> flat over all frequency). I used Matlab function wgn to get it:
> � �wn=wgn(1,10000,1,'linear');
> Does the function above generate a white gaussian noise whose PSD is 1?
>
> Then I did simple experiment to check its PSD. I used Matlab function
> periodogram without any window:
> � �[p,w]=periodogram(wn);
> � �figure; plot(w,p);
> Theoretically, the PSD of a white noise should be flat( or at least flat
> looking in numerical computation). But the plot showed the PSD of wn is
> totally noisy, no flat looking at all. So I got confused about that.
>
> Could you guys check if I made mistake here? Can you figure a way to
> generate white noise whose PSD is 1 in Matlab? Thanks a lot!
>
> Steve
Oh... you must average over hundreds of ensembles.
Reply by Gordon Sande●February 5, 20092009-02-05
On 2009-02-05 12:28:44 -0400, "BreadPaPa" <iamstevewang@yahoo.com> said:
> Hi, all,
>
> I would like to generate a white noise whose power spectral density is 1(
> flat over all frequency). I used Matlab function wgn to get it:
> wn=wgn(1,10000,1,'linear');
> Does the function above generate a white gaussian noise whose PSD is 1?
>
> Then I did simple experiment to check its PSD. I used Matlab function
> periodogram without any window:
> [p,w]=periodogram(wn);
> figure; plot(w,p);
> Theoretically, the PSD of a white noise should be flat( or at least flat
> looking in numerical computation). But the plot showed the PSD of wn is
> totally noisy, no flat looking at all. So I got confused about that.
>
> Could you guys check if I made mistake here? Can you figure a way to
> generate white noise whose PSD is 1 in Matlab? Thanks a lot!
>
> Steve
You have a periodogram just like the name says. It is not a CONSISTENT
estimator as it has no averaging. If it were consistent then it would
have a limiting distribution which got narrower until it was pragmatically
a constant. To get the sort of thing you were expecting you will have
to do some spectral averaging. Probabely the best thing would be to read
a bit more of your text book. The lack of consistency confused a whole
lot of folks back about 1900 but there has been better understanding
since the 1930s.
You could get a lot of periodograms and see if their mean is like what you
expect. The individual periodogram values are distributed as the sum of
2 Gaussians squared or Chi Square on 2 degress of freedom or exponential
depening on which name you prefer.
Or you could do one of the smoothed estimators. But this is such a basic
confusion that it is not clear what level of understanding you have so one
could make a recommendation that you would be able to follow.
Otherwise you got white Gaussian noise.
Reply by Rune Allnor●February 5, 20092009-02-05
On 5 Feb, 17:28, "BreadPaPa" <iamstevew...@yahoo.com> wrote:
> Hi, all,
>
> I would like to generate a white noise whose power spectral density is 1(
> flat over all frequency). I used Matlab function wgn to get it:
> � �wn=wgn(1,10000,1,'linear');
> Does the function above generate a white gaussian noise whose PSD is 1?
Check the documentation.
> Then I did simple experiment to check its PSD. I used Matlab function
> periodogram without any window:
> � �[p,w]=periodogram(wn);
> � �figure; plot(w,p);
> Theoretically, the PSD of a white noise should be flat( or at least flat
> looking in numerical computation). But the plot showed the PSD of wn is
> totally noisy, no flat looking at all. So I got confused about that.
The statistsics of stochastic processes are valid over
double infinites: Infinite numbers of sequences, which
each are infinetly long. You are working with one sequence
which is finitely long.
Rune
Reply by BreadPaPa●February 5, 20092009-02-05
Hi, all,
I would like to generate a white noise whose power spectral density is 1(
flat over all frequency). I used Matlab function wgn to get it:
wn=wgn(1,10000,1,'linear');
Does the function above generate a white gaussian noise whose PSD is 1?
Then I did simple experiment to check its PSD. I used Matlab function
periodogram without any window:
[p,w]=periodogram(wn);
figure; plot(w,p);
Theoretically, the PSD of a white noise should be flat( or at least flat
looking in numerical computation). But the plot showed the PSD of wn is
totally noisy, no flat looking at all. So I got confused about that.
Could you guys check if I made mistake here? Can you figure a way to
generate white noise whose PSD is 1 in Matlab? Thanks a lot!
Steve