Signal Estimation from PSD

Hi,

I am kinda new to signal processing, and I having a problem with PSD.

Given that I have the PSD estimate of a signal, f(x), it is possible to
recover/estimate the function f(x) from just it's PSD?  I am thinking
of ifft, but not sure am I in the right direction.

Cheers,
//

ppirrip wrote:
> Hi,
>
> I am kinda new to signal processing, and I having a problem with PSD.
>
> Given that I have the PSD estimate of a signal, f(x), it is possible to
> recover/estimate the function f(x) from just it's PSD?  I am thinking
> of ifft, but not sure am I in the right direction.

The short answer to your question is No. It is not possible to
reconstruct the signal from the PSD.

A slightly longer answer is based on the periodogram.
Let X[k] be the DFT of the time series x[n]. Then the
periodogram P[k] is defined as

  P[k] = X[k]*conj(X[k]) = |X[k]|^2.

As you can see, the phase information contained in X[k] is
lost, and one can not reconstruct x[n] from P[k]. The best one
can do is to find a sequence x'[n] that has the same PSD.
One way of doing this is to require x'[k] to be minimum phase
(which x[n] may or may not be).

There are plenty of texts on statistical signal processing
and spectrum estimation around. The books by Kay are quite good.

Rune

Hi,

If you use the IFFT, what would you use as the phase?

The quick answer to your question is "no", because the
PSD of a signal is only the magnitude, and you need
both magnitude and phase to reconstruct a signal.

--Randy

Thanks Rune!

Do you have the citation of the books by Kay handy?  As there are too
many books in that topic.

If I want to dig deep on this topic, start with google, what is the key
word that you think I should use?  spectrum estimation doesn't seem to
give me good result.  

Thanks again.

ppirrip wrote:
> Thanks Rune!
> 
> Do you have the citation of the books by Kay handy?  As there are too
> many books in that topic.
> 
> If I want to dig deep on this topic, start with google, what is the key
> word that you think I should use?  spectrum estimation doesn't seem to
> give me good result.  

I hope you can enlighten me. In what situation outside of a classroom 
would one know the PSD without having access to the signal itself?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

ppirrip wrote:
> Thanks Rune!
> 
> Do you have the citation of the books by Kay handy?  As there are too
> many books in that topic.
> 
> If I want to dig deep on this topic, start with google, what is the key
> word that you think I should use?  spectrum estimation doesn't seem to
> give me good result.  

I hope you can enlighten me. In what situation outside of a classroom 
would one know the PSD without having access to the signal itself?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

ppirrip wrote:
> Thanks Rune!
> 
> Do you have the citation of the books by Kay handy?  As there are too
> many books in that topic.
> 
> If I want to dig deep on this topic, start with google, what is the key
> word that you think I should use?  spectrum estimation doesn't seem to
> give me good result.  

I hope you can enlighten me. In what situation outside of a classroom 
would one know the PSD without having access to the signal itself?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������