Time Series Analysis Question from a User?

Question

See below the issues and questions from a JMP user. Any insight anyone can offer would be appreciated.

I am wanting to perform Fourier transforms on my data.  I have found that this is done in the Analyze : Specialized modeling : Time Series : Spectral density.  That part I can do and seems to work just fine.  My issue is that I cannot find good jmp documentation on how to convert from spectral density to signal amplitude.  Could you please help me with this or perhaps pass this inquiry to someone who can steer me in the right direction.

JerryFish · Accepted Answer

Peter, this one is near and dear to my heart.  In my pre-JMP days, I worked in Acoustics and Vibrations.  All about FFT's and spectral analysis.  And in my way-back life, my Masters thesis involved using Time Series to model fan blade vibrations.

A few years ago (pre JMP employment) I presented a paper at one of the Discovery conferences on a Time Series add-in that I wrote.  The writeups are still available on the File Exchange:

https://community.jmp.com/t5/Discovery-Summit-2014/A-JMP-Script-to-Enhance-Spectral-Density-Analysis-in-the-Time/ta-p/21797

I'm not sure why the script itself isn't there, so I'm attaching to this reply.  I think it did what your customer is wanting.  It seems to still work for me (even though it's 5 years old).  Happy to talk with you/customer about it further.

If the customer is just interested in the formula behind the Spectral Density in JMP14, I think it works out to be:

0-pk Signal Amplitude = 5.013 * SQRT(Spectral Amplitude / NSamples)

So if your time signal contains NSamples=1024 samples, and you measure your spectral amplitude (from the Spectral Density plot in JMP) to be 1000 units, then the 0-Pk signal amplitude is:

Signal Amplitude = 5.013 * SQRT(1000 / 1024) = 4.954 amplitude units 0-pk.

Note that I found 5.013 empirically over the last few minutes.  It has to do with the spectral line spacing in the Spectral Density.  I could figure it out given a little time though.  I'll do more on this if you like, but I'm guessing he'll be relatively happy with the addin.

And please remind your customer that there can be "leakage" of energy from the true frequency into the sidebands of the spectrum surrounding the frequency.  So typically you sum the values of all spectral lines that make up the frequency before inserting into Spectral Amplitude in the above equation.