kiki wrote:

> Hi all,
> 
> These two terms from two different domain confused me a lot.
> 
> FT is for deterministic analysis, whereas PSD is the FT of the 
> autocorrelation function, which is for stochastical signal analysis...
> 
> Am I right?
> 
> I am wondering if we use Matlab generate some random signal, and treat it as 
> a dterministic signal, and take its FT, versus using Matlab to take its PSD,
> 
> Should these two things somehow related?
> 
> In what capacity are they related? 
> 
> 
Yes, kinda.

The power spectral density of a signal is the fourier transform of the 
expected value of the autocorrelation function, so you can never 
actually measure it (you can only measure samples of the signal and make 
guesses).

Assuming that you could measure a signal, autocorrelate it, and get a 
result that is largely representative of the expected value of the 
autocorrelation of the signal, you can use the fact that the 
autocorrelation operation convolves the signal with it's time-reversed 
self.  This means that the Fourier transform of the autocorrelated 
signal is the Fourier transform of the signal times the complex 
conjugate of the signal, which is just the amplitude squared of the 
Fourier transform of the signal.

Matlab, I believe, also does some bin averaging, because the Fourier 
transform of a truly random signal has quite a bit of hash on it in the 
frequency domain which generally isn't representative of the true signal.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Hi all,

These two terms from two different domain confused me a lot.

FT is for deterministic analysis, whereas PSD is the FT of the 
autocorrelation function, which is for stochastical signal analysis...

Am I right?

I am wondering if we use Matlab generate some random signal, and treat it as 
a dterministic signal, and take its FT, versus using Matlab to take its PSD,

Should these two things somehow related?

In what capacity are they related?