Hi,
Based on numerical methods, I tried to differentiate velocity signal but without any good results. The velocity signal is sampled as 10Hz.
When I tried to use differentiation method in frequency domain, I was left with the issue of deciding on the frame size of fft and the delay in processing real time signals.
How can I differentiate the real time velocity data in frequency domain? What should be the frame size?
Why do you go to frequency domain? Numerical stability?
If your signal is slow compared to your sampling frequency then a simple delta v / delta t should do the job.
My sampling frequency is 10hz and signal is expected to behave within the pass band of 5hz. Is that slow enough??
No .. your sampling frequency should be at least twice the signal frequency to reconstruct a sinus.I would sample at least at 100 times 5 Hz, so 500 Hz.
Buz memory is for free these days, so sample as fast as you can. You can always reduce the number of points afterwards, but you can never increase it.
I have planned to increase the sampling freqeuncy to 20Hz.
There is inherent noise in the source of the signal which is a speed sensor of magentic type aggravated by drive line oscillations.
That is why I need to differentiate in frequency domain. Now I am confused how big the sample size or frame size should be used for this process without imposing any major delay. Or I may use FIR differentiator and attenuate high frequencies and allow only low freqeuncies upto 5hz.
How to do this without inflicting delay in process??
You have written "signal is expected to behave within the pass band of 5hz", but are you sure it is true?
I think it is not true, because of noises in the source of the signal you wrote.
So, you have to sample faster or you have to use additional low pass filter before analog to digital converter.
If you decide to sample faster, you can use a digital low pass filter before differential algorithm (it is simpler, I think).
I mean the actual signal source is noisy and the actual signal of interest lies within the freqeuncy passband of 5hz.
I tried to sample faster but am now stuck in the way I upsample the signal currently available at 10Hz sampling rate to 100hz or say 500 hz using matlab.
Shall I use inbuilt Matlab functions to upsample??
Is it a good idea to upsample to 500hz and then apply an FIR differentiator filter to the signal??
to prevent loss of data, I would prefer it after differentiation in frequency domain..Moreover I can put saturation to the values of acceleration later after smoothening. Now the real problem starts in deciding the no. of samples per frame to be selected. I am getting tempted for bigger samples size but it creates a lot of delay in my system. Is there any thumb rule on samle size for a time signal when applying such filters??
I believe that you need to apply a low pass filter before you even sample the data. Typically one makes a simple RC filter with the required bandwidth (5 Hz in your case). If you let higher frequencies into your sample-and-hold and digitising circuits, you will get spurious frequencies ("ghosts") in your frequency domain which you will never get rid of. So I believe : Filter first (lowpass), sample thereafter.
I would stay in the time domain. Fit a polynomial (linear or quadratic) using discounted linear least-squares regression then differentiate the fitted polynomial and evaluate it at the desired time offset. If you do the math, you end up with a nice IIR filter. I presented a paper on this just this week! It has equations for the filter coefficients.
Yes, sampling faster would help. And yes, you need lots of high-frequency attenuation for good results, but this is part of the fitting process described above.
Conference Paper Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay
I don't know the details of your measurement, but if the raw data is position vs. time, then it is virtually impossible to obtain useful acceleration results. When I was doing rail gun work I always said "two derivatives of position data is noise." The only reliable acceleration measurement has to start with a true measurement of velocity, i.e. Doppler effect from microwave or laser. Then one derivative is a reasonable measurement of acceleration.
Please refer to this article:
https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design
Article On the Improved Nonlinear Tracking Differentiator based Nonl...
Please refer to this article:
https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design
Article On the Improved Nonlinear Tracking Differentiator based Nonl...
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