Conversion to PSD?

[revesz]

I have a acceleration vs. time and the calculated
acceleration vs. frequency and the displacement vs. frequency dependence.
How do I get the PSD (micron^2/Hz) vs. frequency from any of these data?
Is it correct to take the displacement vs Hz, square it and divide it by the Hz?

Needless to say, I am very new to the vibration science...

Thanks a lot for the help/
Peter

 

[BobM3]

Is it data in a file or a paper printout? If it's data and you can write a program that takes the data as input, then you can come up with a PSD. You need to know what the sample rate was. I believe the process is:

1) Divide the data into frames, say 1024 points/frame.
2) Fourier Transform (FT) the data.
3) Square the FT for each frame.
4) Average the squares from all the frames (for each freq).
5) Divide that number by the frequency resolution (sample rate/frame length).

Not quite sure if I have it right. The Book "Numerical Recipes in C" explains it and has the code for it.

 

[GregLocock]

You'll need to correct the amplitude of the FFT to give the same total RMS energy as the time signal.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[revesz]

>1) Divide the data into frames, say 1024 points/frame.
>2) Fourier Transform (FT) the data.
>3) Square the FT for each frame.
>4) Average the squares from all the frames (for each freq).
>5) Divide that number by the frequency resolution (sample rate/frame length).

Dear Bob,

This is what I have: acceleleration(t) data converted to
the frequency domain with FFT, then divided by omega^2 so
I have displacement vs frequency data set.
Peter

 

[BobM3]

You want to end up with displacment^2/hz.

Don't divide the squared and averaged FTs by frequency^2. Step 5) is referring to the frequency resolution. Say you had data sampled at 204.8 points/sec and you selected a frame length of 1024 points. Your frequency resolution would be 204.8/1024 = .2 hertz. So in the final step you divide your squared and average FTs by a constant, .2 hertz.

Also, most FT code will put half the amplitude in the negative frequencies. Since the negative frequencies are redundant, an easy step is to just keep the positive frequencies and multiply the FT values by 2.

There may be some other gotchas to look out for (windowing for instance). It's been 14 years since I worked for the company that wrote and used this stuff that I don't feel comfortable trying giving too much detailed info.

I assume you are writing your own code? I'd really recommend the "Numberical Recipies.." books. If you are not writing your own code then maybe check into Matlab. Im sure there are other programs out there also.

 

[GregLocock]

Sorry "RMS energy" is redundant and unnecessary. I should have said "energy".




Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Vibac]

In other words: Divide the power spectrum by the measurement resolution including a correction for the data window: 1.5 for Hanning window and 1.0 for no window.

 

[revesz]

Thanks guys for the advice!
Peter