PSD Computing 1

[lucsax]

Hi everybody,
I need to evaluate the PSD from a "time history" signal.
Now I'm able to make the FFT of the signal (the FFT is "normalised", i.e. the spectum of an harmonic signal freq f amplitued A return a single value at freq f and of aplitude A).
Can anybody explain how to go further in order to obtain a PSD?
Thank you very much in advance
Luca

 

[MikeyP]

Multiply the complex value at each spectral line by its conjugate and divide each spectral line by the difference in frequency between two adjacent lines.

M

 

[baigazin]

The calculation of PSD has many specialities. Simple FFT transformation solves the problem (theoretically), but in practics there are more problems.
E.g.: time signal has finite length, while FFT decompose signal into a number of SIN/COS functions which are infinite, and to make it the time signal is supposed to repeate infinitely which leads to abrupts in begin/end of the signal. Such an abrupt causes additional sinusoidal waves to be added. To resolve this problem time signal is to be multiplied by 'window' and after transformation it is to be scaled to balance the common power.
Another problem: computing PSD has a property that increas of time signal *doesn't increase the precision of PSD*. To overcome it the time signal is diveded into several segments for which PSD is calculated separately and then averaged by segments. This method is known as 'Welch method'.
All these and many other problems are described and resolved in MATLAB program. There is a special matlab's toolbox called 'Signal Processing Toolbox' which involves preprogrammed functions of PSD calculations. I used to take MATLAB and this toolbox in free evaluation; look their website (

http://www.mathworks.com),

maybe this possibility still available. There is also free documentation to this toolbox describing PSD computation, including those I have written above:

http://www.mathworks.com/access/helpdesk/help/toolbox/signal/signal.shtml

 

[MikeyP]

Just an aside:

The matlab functions psd and csd are the only places I have ever seen this method described as "Welch's method". Almost everyone else calls it "the Fourier transform estimation method". I have sometimes described it to people as Welch's method and they just stare at me blankly!

M