How to add spectral amplitude values in a band

[CamJPete]

Hello. I'm relatively new to vibration analysis, and I am trying to understand how to bin a narrow band FFT into one-third octave bands. My measured data has units of lbf, and lbf-in. Most of the information on this topic is acoustics related, but I can't find much for other units that aren't acoustic-related. For example:

https://www.eng-tips.com/viewthread.cfm?qid=124244.

I have bits of principles and information floating around in my head and I haven't fully connected all the dots yet.

Most of the information is how to convert a narrow-band PSD into one-third octave bands. It seems that this is done simply by taking the area under the curve of the PSD between the low and high frequencies of each band. This would give the lbf-rms value for that bin. Then...I think I would then take the lbf-rms multiplied by the sqrt(2) to get the lbf-peak for a given one-third octave band(?). Correct me if I misunderstand this part.

For my problem at hand, I have raw reaction force / time history, and I don't want to have to calculate the PSD to bin in to one-third bands. How do I do this with amplitude instead of power? That is, if I have amplitudes (not power) as a function of frequency, how can I bin those amplitudes into one-third bins? My guess is to take the square root of the sum of the squares of each amplitude within a given one-third band. Is this right? It seems to make sense, as it is type of converting the amplitudes to a power by squaring, which are then summed, then returned back to amplitude by square rooting. (It seems it isn't ever a PSD because it was never normalized by Hz, so in that sense it doesn't get converted fully to the PSD?).

Thanks for your time.

 

[GregLocock]

If you have the raw time history then you can check that the total power in your spectrum is the same as that in the time history.

Cheers

Greg Locock


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[CamJPete]

Thanks Greg. After some trial and error with some test data today, I feel good about my earlier hypothesis: take the RSS of the FFT values within a one-third octave band. I realized this is because the square root of the area under a frequency step (say from 20 Hz to 21 Hz) in the PSD is the same as the amplitude of the FFT plot (say at 20.5 with a bandwidth of 1 Hz). If I want the one-third octave band, I just need to RSS all the points in the FFT from fLower to fUpper.