# Unit of enery after taking FFT of velocity data

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Mainul Hoque on 11 May 2015
Commented: Thomas Koelen on 11 May 2015
Dear all,
I was taking the fft of velocity time data. But I am confusing about the unit of energy after taking fft.
For Example:
velocity have the unit of m/s.
I take the FFT of u(t) then I get u(f). i,e u(f)=sum[u(t)exp(-j*2*pi*f*t)] and calculate the energy over frequency domain by multiplying u(f) with the conjugate of u(f). i.e.
E(f)=u(f)*conj(u(f))
Then my question is what is the unit of E(f). Is that m2/s or m2/s2.
and what is the unit of u(f)?? Is that m/s or m.
Could anybody clear me about the above problem and give me some reference.
Thanks
Pavel

Thomas Koelen on 11 May 2015
It's still a velocity. If you do a continuous Fourier transform, you go from signal to signal integrated over time, which is signal per frequency, but in a discrete Fourier transform you're just summing discrete velocities with coefficients, and the result is still a velocity.
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Thomas Koelen on 11 May 2015
Yes :)