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FFT Unit Output Interpretation...

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GearHead3

Mechanical
Joined
Sep 9, 2010
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Location
US
Hello everyone,

I am new to this forum as of today.

I have a question regarding the interpretation of output units when converting a time domain signal into the frequency domain via an FFT (Fast Fourier Transform).

Specifically, let’s assume the conversion of a typical time-history random vibration signal that was measured using any field data acquisition system with an accelerometer. For this discussion, the DAQ output unit of measurement is “G” (gravity/acceleration).

My question is: When viewing the display of the magnitude spectrum for this signal using FFT instrumentation, is the unit of measure for the Y-axis (magnitude) on the frequency domain plot automatically considered to be G-peak, or G-rms?

The reason for my confusion stems from the following – I will try to be as clear and concise as I can:

When an FFT is crunching the measured signal values at each line of spectral resolution (frequency bin)… the process of signal convolution between cosine and sine mapping is very similar to calculating RMS (root-mean-square), but in actuality, it (looks to me) more like the calculation process is really RSS (root-sum-squared) instead.

For example – at any given frequency bin of spectral resolution….

Step 1 – the FFT process multiples each measured data value in the signal sample by the mapped cosine function for that specific frequency bin.

Step 2 – the FFT process sums all of these new values for the table of samples to create an aggregate total. This aggregate sum of cosine multipliers becomes the REAL part of the FFT complex number.

Step 3 – the FFT process repeats the same procedure for every measured data value by mapping & multiplying against the inverse sine function. The sum of this (separate) table of numbers then become the IMAGINARY part of the FFT complex number.

Step 4 – the FFT process then begins the calculation of absolute modulus of the complex number by squaring the REAL aggregate sum (and) squaring the IMAGINARY aggregate sum.

Step 5 – the FFT process adds the two squared aggregates together (Real + Imaginary).

Step 6 – the FFT process then calculates the square root of this total.

Step 7 – the FFT process then divides this newly created square root by the number of original data values in the sample. This value is considered to be the “half magnitude” prior to discarding the information beyond the folding frequency (nyquist).

Step 8 – the FFT process doubles the half magnitude value to display the full magnitude after discarding the negative frequencies beyond the folding frequency.

My Conclusion: This final FULL magnitude value is still in the same unit as the original time history signal [ie: G], BUT my uncertainty is whether it is G-peak, or G-RMS???

I already realize that by squaring all of these full magnitude values in the FFT display – it will show the POWER spectrum, but even so, would this be considered Peak-Power, or RMS-Power????

I guess what I’m curious to understand is… (If by inherent nature of the raw FFT calculation during each frequency bin) does the natural output of the FFT process automatically convert the primary unit type to RMS instead of peak?

I have surfed the web and searched manuals & books endlessly – but have not found an answer to this simple question. What am I missing in my understanding???

I’m not a wizard regarding differential equations, so any replies; please try to keep answers in layman’s terms (as best possible).

Thanks!

GearHead3

 
Try the Mechanical Acoustics/Vibration Engineering Forum.
 
don't think the viibration forum will be much help, to effectively use fft you need to understand the math, otherwise they are just traces on the sceen
 
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