# Help needed in analyzing FFT acceleration peak

1. Oct 30, 2010

I have collected time-domain acceleration signals from the test rig through an accelerometer. Voltage signals are scaled to acceleration signals based on voltage sensitivity of accelerometer. Please refer the link given at the last to get the link for PDF attachment to see the time domain acceleration signals. Acceleration varies from 4 to -13 m/sec2. Later FFT analysis is done in Matlab software. Please refer to the link given at the end to get the link for attached PDF file to see the Frequency-domain acceleration signals. But here I got the acceleration peaks very high (of the order 70-100 m/sec2). Kindly suggest me whether the acceleration peaks convey the meaning ful result? Whether some kind of normalization is required for Y axis (acceleration peak) of the frequecy domain signal? Please guide me how to present the acceleration peaks in a meaning ful way?

Waiting for ur valuable suggestions...

http://imechanica.org/node/9195

Last edited by a moderator: Apr 25, 2017
2. Oct 30, 2010

### marcusl

You have asked a question with no easy answer, since taking a spectrum looks easy but rests on a mass of details and assumptions. The spectrum in your attachment has many fewer points than your data set; how did you calculate it? Did you split the data into intervals, calc the spectrum of each, and average? (e.g., periodogram). Is your spectrum complex? (It should be.) Are you showing just the real part? The magnitude? A classic FFT will also show negative frequencies; where are these? What normalization are you using? All of these affect the absolute magnitudes.

3. Oct 31, 2010

Thank you for replying!..I collected both time and voltage (scaled to acceleration) data. Hence I do have data about time interval also. But I have used 1024 datapoints to calculate FFT in Matlab. Then I calculated FFT magnitude, i.e. absolute of FFT. The amplitudes you are seeing in the figure are FFT magnitudes. Normalization is not used.

4. Oct 31, 2010

### marcusl

Ok. If the number of time and frequency domain points is the same (1024), then you can do a simple test to check the normalization. Remember from Parseval's theorem that the total energy in each domain must be the same. Check, therefore, that

$$\sum_n{|f[n]|^2}=\frac{1}{N}\sum_k{|F[k]|^2}$$

Also the units in the frequency domain are different than the time domain. They should be volts/sqrt(Hz) so that the power spectrum |F[k]|^2 has units of energy.