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Integration best done in time domain or frequency domain?

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Junior Member level 3
Feb 13, 2007
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integration in frequency domain

New to DSP.

Need to convert a data set from acceleration to velocity.

Is the integration process best done in time domain or frequency domain? Haven't found a DSP text that addresses this question.

integration frequency domain

Acceleration is the rate of change of velocity with respect to time, thus you have to be in the time domain.

fft integration

So the process would go:

1. Collect phase based accel data
2. Numerically integrate to velocity
3. Perform FFT to obtain amplitude and phase


frequency domain integration

I'm not a DSP man so I'm not sure if I can be much more help to you, but I'm not sure you can phase from an FFT. You'll get a spectrum of frequencies contained in the signal and their power. You may of course, have a experimental setup such that the power of a particular frequency gives you an indication of phase.
I would be quite interested to know if there is a way of extracting phase data from an fft!

integration in the frequency domain

I'm new to DSP myself.

One guy told me that while frequency and amplitude are obviously present in the real part of an FFT, phase can be gleaned from the imaginary part of an FFT.

integrating acceleration data

That maybe possible right enough.

If you can find out how to do that, and you have access to Matlab or similar then you should have no problem finishing the task.

integration time domain

In my opinion, the operation can be done either in time or frequency domain because the integration operation is commutative. Note that you have two integration operation, one is due to Fourier transform, and other is due to integration from acceleration to velocity. This can be done:

1st method (your method):
1. Collect phase based accel data
2. Numerically integrate to velocity
3. Perform FFT
4. Obtain amplitude and phase

or, 2nd method:
1. Collect phase based accel data
2. Perform FFT of the accel data
3. Numerically integrate of accel data to velocity data in frequency domain
4. Obtain amplitude and phase of 3rd step


integrate in frequency domain


integrator in time domain

I already done it in time domain
it is very easy to add sample by sample
As I have to find 4 frquencies(velocities) so I use goertzel algorithm to find them in real time

best regards

frequency domain of an integrator

Dear naresh850,

I am a little confused: you wrote that you did the processing in time domain but then you wrote that velocity recognition is based on Goertzel algorithm. But this is equivalent to saying that the processing is in Frequency domain, because the Goertzel is a simplified method to calculate FFT frequency bins.
Please could you clarify?


time domain integrator


In time domain u can done acceleration to velocity conversion in real time i.e sample by sample.

And also u can fine specific frequency in real time by goertzel algorithm.

Thats what i want to say.

In regard to time domain vs. frequency domain, Its depend on ur application which method has to choose.

best regards,

integrating acceleration to velocity fft

To integrate from acceleration to velocity do the following:
Do acomplex FFT on the accel signal
Scale the FFT components with a factor 1/(2*pi*f)
Do the inverse FFT

frequency integration to get phase

u choose ur self because integration in time is equal to devision in frequency domain,choice is urs

integrate in frequency domain.

Integration of raw acceleration data in time domain may introduce integration error. It is possible to reduce some of this error by performing high pass filtering on the data prior to integration.

I am not certain on the best method to get velocity magnitudes in the frequency domain from calculating the acceleration magnitudes in the frequency domain.

I'm not sure you can simply divide acceleration magnitudes from the FFT by 2pi*f for each frequency (assuming 1 Hz resolution) to get velocity magnitudes in the frequency domain...

i.e your are trying to exploit this relationship
d( s(t) )/dt = (i 2 pi fn)*S(fn)
int( s(t) ) dt = S(fn)/(i 2 pi fn)

Any subject matter experts want to educate us?

matlab integrate acceleration

u'll get spectrum like low pass filter if u choose frequency domain n if u choose time domain u'll get a differentail equation

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