Power Spectral density

Dear All,
I am strugling writing a matlab code to present the PSD of a random
sequence of data.
I am not getting a smooth curve like I see it in some textbooks. Could
anyone help me with Matlab code where I can get the PSD graph which look
like a continues curve.
Thans a lot
Regards
khmaies

khmaies wrote:
> Dear All,
> I am strugling writing a matlab code to present the PSD of a random
> sequence of data.
> I am not getting a smooth curve like I see it in some textbooks. Could
> anyone help me with Matlab code where I can get the PSD graph which look
> like a continues curve.
> Thans a lot
> Regards
> khmaies

How much averaging are you doing?

"khmaies" <khmaies@gmail.com> wrote in message
news:xemdnf_pfeOyOfbenZ2dnUVZ_s2dnZ2d@giganews.com...
>
> Dear All,
> I am strugling writing a matlab code to present the PSD of a random
> sequence of data.
> I am not getting a smooth curve like I see it in some textbooks. Could
> anyone help me with Matlab code where I can get the PSD graph which look
> like a continues curve.
> Thans a lot
> Regards
> khmaies

You won't get a smooth curve - even if you average unless the statistics are
stationary. You can average like this

P(i)=beta*P(i-1)+(1-beta)XX^

where ^ is complex conjugate of the freq vector X and beta is a forgetting
factor. P is the periodogram or Spectral Density estimate at FFT frame
i=1,2,3...

McC

clc
close all
clear

% number of samples
N=1000;
% create data with filter
num=1;
den=[1 -0.5 0.2]
x=filter(num,den,randn(1,N));
% do LPC analysis to estimate inverse filter
[den_hat,num_hat]=lpc(x,2);
den_hat=real(den_hat);
num_hat=sqrt(num_hat);
% calculate non-parametric power spectrum
Sxx=abs(fft(x,2*N)./(2*N)).^2;
% calculate parametric power spectrum
Sxx_parametric=(abs(fft(impz(num_hat,den_hat,2*N))).^2)./(2*N);
% plot results
plot(Sxx);
hold;
plot(Sxx_parametric,'ro');
hold;






"khmaies" <khmaies@gmail.com> skrev i en meddelelse 
news:xemdnf_pfeOyOfbenZ2dnUVZ_s2dnZ2d@giganews.com...
>
> Dear All,
> I am strugling writing a matlab code to present the PSD of a random
> sequence of data.
> I am not getting a smooth curve like I see it in some textbooks. Could
> anyone help me with Matlab code where I can get the PSD graph which look
> like a continues curve.
> Thans a lot
> Regards
> khmaies 

>clc
>close all
>clear
>
>% number of samples
>N=1000;
>% create data with filter
>num=1;
>den=[1 -0.5 0.2]
>x=filter(num,den,randn(1,N));
>% do LPC analysis to estimate inverse filter
>[den_hat,num_hat]=lpc(x,2);
>den_hat=real(den_hat);
>num_hat=sqrt(num_hat);
>% calculate non-parametric power spectrum
>Sxx=abs(fft(x,2*N)./(2*N)).^2;
>% calculate parametric power spectrum
>Sxx_parametric=(abs(fft(impz(num_hat,den_hat,2*N))).^2)./(2*N);


Fourier transform of a random process is another random process :)

what you need to do is perform the above several dozen times (at least)
and then average the resulting FFTs - only then will you see the
smoothness start to appear.

> Fourier transform of a random process is another random process :)
>
> what you need to do is perform the above several dozen times (at least)
> and then average the resulting FFTs - only then will you see the
> smoothness start to appear.


Yes, but LPC-analysis will give you a smooth approximation of the 
non-parametric power spectrum...

Lars Hansen wrote:
>>Fourier transform of a random process is another random process :)
>>
>>what you need to do is perform the above several dozen times (at least)
>>and then average the resulting FFTs - only then will you see the
>>smoothness start to appear.
> 
> 
> 
> Yes, but LPC-analysis will give you a smooth approximation of the 
> non-parametric power spectrum...
> 
> 
> 
Are you saying that you don't need to average?

There are lots of ways to smooth but they aren't necessarily accurate.

"Stan Pawlukiewicz" <spam@spam.mitre.org> wrote in message
news:dkiffa$ic7$1@newslocal.mitre.org...
> Lars Hansen wrote:
> >>Fourier transform of a random process is another random process :)
> >>
> >>what you need to do is perform the above several dozen times (at least)
> >>and then average the resulting FFTs - only then will you see the
> >>smoothness start to appear.
> >
> >
> >
> > Yes, but LPC-analysis will give you a smooth approximation of the
> > non-parametric power spectrum...
> >
> >
> >
> Are you saying that you don't need to average?
>
> There are lots of ways to smooth but they aren't necessarily accurate.
>
Not if you use parametric methods. LPC is not so good at measuring zeros
since it is an all-pole method. There are pole-zero techniques which require
more computation.

McC

>>
> Not if you use parametric methods. LPC is not so good at measuring zeros
> since it is an all-pole method. There are pole-zero techniques which 
> require
> more computation.
>
> McC
>


That's true, but you can just increase the order of the LPC-analysis to 
model
the zeros... - but you are right...pole-zero techniques are probably more 
efficient

khmaies wrote:
> I am strugling writing a matlab code to present the PSD of a random
> sequence of data.
> I am not getting a smooth curve like I see it in some textbooks. Could
> anyone help me with Matlab code where I can get the PSD graph which look
> like a continues curve.
Try Rainbow ... http://digitalCalculus.com/page/593045 ... it has some
10+ algorithms for a PSD and these vary like crazy in their results.
Finding key peak (i.e. frequencies) is hard in itself.

Good luck hunting.

Phil