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
PSD of white noise NOT flat?
Started by ●February 5, 2009
Reply by ●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 ●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! > > SteveYou 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 ●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! > > SteveOh... you must average over hundreds of ensembles.
Reply by ●February 5, 20092009-02-05
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
