hi

1. Downsampling requires a pre-filter to eliminate aliasing  depending on the frequencies involved. A very simple example is say fsig=6hz  , fsampling= 36hz . D=2 then new fsamnew= 36/2= 18 . This is still > 2*6 =12hz (nyquist condn fsig  < fsam/2) so no filter is needed.No information is lost.

2. If we downsample  by D= 4 then fsamnew=36/4 = 9hz , here fsig=6hz>9/2 hz so we need a prefilter. We lose information.

3. Please see attached pdf..hope it is of help.

Cheers

hi

1. Downsampling requires a pre-filter to eliminate aliasing  depending on the frequencies involved. A very simple example is say fsig=6hz  , fsampling= 36hz . D=2 then new fsamnew= 36/2= 18 . This is still > 2*6 =12hz (nyquist condn fsig  < fsam/2) so no filter is needed.No information is lost.

2. If we downsample  by D= 4 then fsamnew=36/4 = 9hz , here fsig=6hz>9/2 hz so we need a prefilter. We lose information.

3. Please see attached pdf..hope it is of help.

Cheers

Why use only the latest sample produced by the sensor in the current control-loop update? I think you would be better off using all of the samples output by your sensor.

If you suspect your sensor introduces high-frequency noise (often the case), then you could apply a low-pass filter to the sensor samples to remove it, before sending the output to the controller. When designing your filter, you may need to make sure you don't introduce too much of a low-frequency phase lag though, as it may 'eat' into your stability margins. There is usually a trade-off here - good high-freq attenuation is usually achieved using longer delays.           

You could process your recent sensor samples, acquired since your previous control update, as a block, using an FIR filter, on each new control update; or you could apply an IIR filter recursively, with a longer 'memory', and just use the latest filter output when the control action needs to be calculated. 

The simple way is to average the five samples. It can be proved that the moving average (MA) filter has exactly the banwidth you desire for antialiasing. Usually the MA filter has a bad frequency response (magnitude ripple in the high spectrum) but in this case it is just perfect (you will not see the high spectrun in the downsapled signal).

Take care

Andrea 

Thank you, Andrea! My first solution was to do a moving average filter.

The second option I'm thinking about is to introduce a low-pass filter. However I have strong requirements on the stability margins, and it is reducing considerable the SM. 

May I have to do a trade-off beetween the roll-off filter and bandwidth of the system (stability vs performance).

Thank you for all your answers.

Try designing your low-pass filter using least-squares polynomial regression. This gives you superb phase control in the very low-frequency region and applies massive gain attenuation everywhere else. Your moving average (MA) filter is just a limiting case of this!   

@Hugh Lachlan Kennedy 

Your suggestion seems very interesting and unusual. .Would you care to give some hints/ref /simple example on the design method?

Thanks

 Cheers

I have written a few papers on this. Some have been accepted and some are under consideration (so slow!). Some of the older stuff has already been uploaded to my RG pubs; but I should also upload some of the newer (better) stuff too; along with a tutorial-style summary perhaps.

I  work on many different problems and I now use this family of filters for everything! If you are just interested in the low frequencies, they give you lots of response and realization options.   

e.g. ...

Article Recursive Digital Filters With Tunable Lag and Lead Characte...

Article Multidimensional Digital Smoothing Filters for Target Detection

I uploaded this just then. It's a better overview - more of a focus on the general design framework than on application ....

Research Generalized IIR Savitzky-Golay Filters: Derivation, Paramete...

@Hugh Lachlan Kennedy

Thanks a lot for the prompt reply.The tutorial would be most welcome,

preferably with low tractable order for trying out in Scilab.

Cheers

... that's fine. I have a shorter paper that just looks at fitting quadratic polynomials. I have found that they are sufficient for most applications. It includes tables with equations for the filter coefficients for causal and non-causal, smoothers and differentiators. All you need to do is plug in your pole location (p, real & repeated, 0

 @Hugh Lachlan Kennedy

Thanks..yes ..would look forward to it..still an algorithmic exposition would be welcome so modifications can be attempted. and one can perhaps see its possible extended applications

Cheers

Adolfo,

In Audio recording, it is common with a ADC  to use "oversampling" at for example 256 f when capturing a signal that is ultimately output at f. The reason is that it avoids expensive analog filters before the sampling and replaces then with a digital low pass  filter after the sampling.  Search for multi-rate filters to see the details.

So yes- a digital low pass filter between the sampling and control loop is the answer.

Paul

What is suggesting Hugh is really interesting.

What I can add on that, in the real field, and in most of the applications, prior to start, the modeling of the noise can give you more opportunities to apply the best choice.

For example if the noise is comparable to a burst generator or something like, a non linear filter is much better than every linear, and a pre filter could be a good option prior to apply the filter. In short, considering an oversampling above the dynamics of the controlled variable, the pre filter should remove the samples for which the variations are not admissible, considering its own dynamics, so replacing it by the latest valid sample. 

cheers

Alessandro Finezzo

I am mising an answer that explains the principles:

Whenever you (down-)sample a signal, you get aliasing if you violate the Shannon theorem. That is, if your sampling rate is less then twice the highest frequency of the signal.

In your case, the highest frequency of the signal as well as the (down-)sampling-rate are unchangable. If the Shannon theorem is not violated, you will not get any aliasing. So: Do you get aliasing?

If yes, and if this is unacceptable for you, you can still throw your sensor away, don't you? :-)

An alternative is to bandlimit the signal below half of the sampling rate (note: in practice, a factor of 5-10 is often applied). This can also completely eliminate aliasing. BUT HERE you change your signal! If this is also unacceptable to you, you are lost. If loosing some information on the sensor signal by filtering it is okay for you, it is always a trade-off between aliasing and information loss.

So, first identify IF you have aliasing at all. Then decide, how much aliasing and how much information loss is acceptable to you. Then go and find the filter that best fits your needs (e.g. ease of implementation, CPU load, smoothness or other filter properties). There is, in general, no one-and-only-answer like "use my filter and with that you'll always have the best solution available"...

Maybe you know all of that already, then sorry for wasting your time - but your question sounded to me as if you should first get the theory somewhat clearer...

EDIT: typos

Dear Adolfo, the MA filter is already a low pass filter. It is a FIR filter. As alternative you can use an IIR setting the digital band to 0.1 (= 1/5 * 1/2). The digital band is usually between [0 0.5]. 

About control:

If you use the MA you can have a considerable phase delay (which is constant because of the linear phase response) that will reduce the phase margin. Instead using an IIR you can take advantage of (1) lower order (2) zeros to reduce the phase delay.

As advanced alternative there also exists certain "zero delay" filters/observers. 

in response to martin: loosing some information is already implied by downsamplig. Filtering before downsampling should be a must (except in control applications if you have very low delay margin).

Andrea, why? If I have a signal that has e.g. 10kHz as "highest" frequency component, and my original digitalization was at 1MHz sampling rate - and now I downsample with 100kHz - how will I loose information? Thanks, Martin

Dear Martin, yes in that ideal case you are right. In the practice some noise (even low) can be present in the high spectrum and this may generate low frequency noise in the downsampled signal. Better to avoid.

Hello again Narasim Ramesh - here is that short paper with coefficients for low-order low-pass IIR filters, with configurable group delay,  I was talking about a while ago ... 

Conference Paper Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay

Hugh Lachlan Kennedy

·thank you

Cheers