Frequency domain integration and differentiation

I'm learning about fourier analysis and am experimenting with integration and differentiation in the frequency domain.

For test cases in the time domain, I generate 3 single frequency data sets: acceleration, velocity and displacement.


Next, I do an FFT of the time domain velocity data,
then integrate in the frequency domain,
then inverse FFT back to time domain and
compare with the test case displacement data.


Next, I do an FFT of the time domain velocity data,
then differentiate in the frequency domain,
then inverse FFT back to time domain and
compare with the test case acceleration data.


Both test cases work, but with a lag (lead?) in time. Since my test data is periodic, I can do a circular shift to get an exact result.

However, the time lag/lead is frequency dependent.

How do I handle an arbitrary signal?

For a 512 sample FFT, do I generate 256 time signals,
apply a separate circular shift for each frequency,
then add all 256 time signals together?

Or have I missed something?

Thanks, RIH5342
.

Relevant Pages

  • Re: FFT with matlab
    ... This new function is a very well known FFT!! ... a so called "real TF" of u0 on a frequency domain between ... matlab (engineer or unity). ... lets return in the time domain. ...
    (comp.soft-sys.matlab)
  • Re: Linear phase and impulse response symmetry
    ... frequency domain (nonconstant group delay) and non-symmetrical impulse ... response in time domain? ... A signal that has even symmetry around 0 will have a Fourier transform that is purely real with even symmetry, ...
    (comp.dsp)
  • Asking for help: how to represent differential equation of DPSK signals correctly in MATLAB
    ... non-return-to-zero DPSK signals (differential equation in time domain ... is more easily solved by FFT in frequency domain). ...
    (comp.soft-sys.matlab)
  • Re: Experiments that measure frequency domain
    ... information with a small number of frequency domain measurements. ... time domain - think about how many samples in the time domain over what ... Suppose you have a metal plate, and it resonance ... A handful of frequency domain measurements will give you both f0 and Q, if you know approximately what f0 and Q are. ...
    (sci.physics)
  • Re: Frequency domain integration and differentiation
    ... integration and differentiation in the frequency domain. ... For test cases in the time domain, I generate 3 single frequency data sets: ... Next, I do an FFT of the time domain velocity data, ...
    (sci.math.num-analysis)