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I have 1000 Hz time series data for acceleration (512 data points), which I want to convert to velocity. I am trying to use the omega arithmetic method to achieve this. Following are the steps I am taking:

  1. Converting the acceleration-time data to its DFT.
  2. Converting the acceleration DFT to velocity DFT using the omega arithmetic formula(dividing each DFT value by i * omega (i.e. 2 * pi * i * freq))
  3. Taking the inverse FFT of the velocity DFT to get velocity-time data.

These steps can be seen in the picture above. I am using numpy's FFT functions, and not normalizing the DFT to avoid any confusion.

My question is: Why are the velocity values so low in the velocity-time plot? Am I making any mistake in my steps?

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  • $\begingroup$ Have you accounted for the DFT scaling? $\endgroup$ – A_A Aug 30 '18 at 11:24
  • $\begingroup$ @A_A No...I figured that since taking an ifft of the original unscaled DFT reproduces the original time-domain signal, I should not scale it. Am I wrong in thinking this? $\endgroup$ – Saurabh Shirodkar Aug 31 '18 at 4:47

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