Problems with waveform integration

[crimolvic]

in time domain the influence of integrating the noise (area under the curve) is preety insignificant compared with the real components of the vibration signal.

in the frequency domain, as you say, the same noise is present and though its influence in the amplitude is not significant, it is in the phase of the components. thus, when you perform the inverse fourier transform, what you do is the sum of cosines with the frequency and amplitude given by the amplitud spectrum (little distortion) and with a phase given by the phase spectrum (lot of distortion), so, what you have is a waveform with the same cosines of the integrated signal but added in the times that they should, thus you have a signal that is quite different of the integrated signal.

in the attached llb is the procedure that i have mentioned early and the two files that contains the corrections curves for boths simple and double integration

greetings, CJMV

[rpursley8]

Process the data in the frequency domain as real/imaginary components as opposed to amplitude/phase. It is hard to work with phase information, but doing signal processing on the real/imaginary components isn't too bad.

Most of the variations in the phase are usually at locations where the amplitude is low and so the noise at that frequency is of the same order of magnitude. If your signal of interest is located at these frequencies and of such low amplitude, you have more of a problem than filtering will fix. Either oversampling or ensemble averaging will be required to reduce the noise.

If there is sufficient signal present at the frequencies of interest, then the phase at those frequencies should be pretty stable.