Problems with waveform integration

[crimolvic]

What I need to do is waveform integration from an acceleration vibration signal to a velocity or displacement signal.

To take the signal to velocity, I first filter the acceleration signal (HPFilter, 5Hz) to remove any offset and the perform the integration.

To probe the method, I use a signal composed by one sine WF with amplitude 1. The test consist in vary the frequency of the sine WF and evaluate the value obtained by the FFT of the integrated signal.

For a freq of 10 Hz, i obtained a value of 0,015931 which is nearly the expected 1/(2·pi·10)=0,015916
for a freq of 150 Hz, i obtained a value of 9,8130e-4 instead of the expected 1/(2·pi·150)=1,061e-3
for a freq of 450 Hz, i obtained a value of 7,91922e-5 instead of the expected 1/(2·pi·450)=3,537e-4

as you can see, higher the frequency, higher the deviation from the expected value. i am triyng to get this solve, but in this moment i don't know why this phenomenon occur.

any help will be well recibed.

CJMV

[altenbach]

Do all your sine WF contain an integer number of periods?

[crimolvic]

Yes, i am taking a 1 second signal for all the tests.

[chrisger]

hi there

can we have some code please?

best regards
chris

[johnsold]

A high pass filter does not perform integration. It may be more like a differentiator.

Lynn

[crimolvic]

yes, here is the code of the tests that i am performing, you can perform the experiment described above.

let's keep doing comments so we can reach an agreement on this waveform integration matter.

regards to all

CJMV

[chrisger]

hello,

increase the sampling rate. with 10.000 smpls/sec you get

f exact meas.
10 1,591e-2 1,593e-2
150 1,061e-3 1,060e-3
450 3,537e-4 3,512e-4

best regards
chris

[crimolvic]

yes, but now i encourage you to try with a frequency of the sine waveform of 4500 Hz. the values are:

4500Hz 7,91922e-6 of 3,5368e-5 expected.

the idea is that when you aquire some vibration signal, you have a lot of sine waves and you want to know the amplitude of all of them precisely, in spite of its frequency

[chrisger]

yeah sure,

but to acquire a signal with a adequate accuracy you need to sample the signal with a rate much higher than the frequency of the signal. you can't integrate the signal when one cycle is sampled with just 2 or 3 samples. you have to find out the maximum frequency of a signal that can occur and then define the sampling rate according to that.

best regards
chris

[crimolvic]

OK, that's a really good point, i am agree with it.

do you have made a study of the relationship between the sampling frequency and the maximum frequency of the signal?.

i am going to make it anyway, but to compare...


another point related to the waveform integration:

i rote in an application note that it is recommended to use a FIR filter instead of an IIR because it has less phase distorition of the signal. however, if you ask for the filter information and plot the "phase H(w)", you will se a big distortion in phase introduced by the filter.
in the other hand, if you do the same thing with an IIR filter, you will find that the phase distortion is less.
conclusion: i am using an IIR filter with a Fc of 5 Hz.

greetings
CJMV