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Calculating FFT using the FFTAverageType variable in DIadem

Hi,

 

I have some doubts about how should I use the averagingType variable. I want to define this variable as "Arithmetic" and get the combined FFT of two trials of the same process, i.e I have two signals which represent the same process.

 

What I do is just calculate the FFT of each signal separately. Then I calculate the amplitude of each FFT signal and finally i combine these two signals by doing the mean for each amplitude. I.E if i have signal1FFT = (1 , 2 ......23 ) and signal2FFT = (2,4, ...43 ) the resulting signal should be ( 3/2 , 6/2 ...... 66/2 )

 

Am I correct about what this averaging type variable does? When i try to do the same in other mathematic programs I get different results but I don't know exactly what I am doing wrong,

 

Thank you so much for the help!

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There are several ways to approach averaging in the FFT environment.

 

FFTAverageType is should be "Arithmetic" which means that all FFTs are weighted equal.

The Exponential averaging is kind of a running average for special calculations which are typically done during a running measurement.

 

Much more important is the parameter in "Calculate average from:" (Amplitude or Autospectrum)

Amplitude is giving a linear result and Autospectrum is giving the result based on squared values. The squared result is the correct result from an energetic point of view.

 

Example:

If you have a sine with a peak of 2 for one second and a peak of 4 for another second, you might want to get and averaged peak of 3.This might be wrong.

 

The RMS value of a sine with a peak of 3 would be 2.121.

The RMS which is representing the energy in a signal is the root of the average of the squared values. The RMS of a signal with half the time 2 and half the time 4 is 2.236. This means, that a sine with the peak of 3.162 for two seconds has the same RMS as the signal with a peak of 2 and 4 for one second each.

 

If you average FFTs in DIAdem you need to decide between the linear average (based on the peak Amplitude) and the energetic correct squared average (based on the Autospectrum). Right or wrong depends on your circumstances.

 

Usually, other mathematic programs are giving you the choice to decide or they might just use one or the other method.

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