Differentiator with FIR filter
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From: Dinne on 11 Feb 2010 13:25 Dear all, I need to calculate an acceleration signal from a signal containing speed samples. I have been looking into using FIR differentiators. Especially the article http://www.dsprelated.com/showarticle/35.php seems interesting. When comparing FIR differentiators, it is probably not enough to look at just the frequency magnitude and phase delay response. For example one can use a simple forward difference scheme or a more complicated five point difference scheme. The latter will result in smaller errors. (http://oregonstate.edu/instruct/ch490/lessons/lesson11.htm) In http://cnx.org/content/m28304/latest they use a filter window to smooth the frequency response of a differentiator. I do not understand however why this approach would be better or worse than the differentiator described in http://www.dsprelated.com/showarticle/35.php. No my question is: Which other graph's and figures should one calculate to compare the quality of a FIR differentiator? What would be the FIR differentiator equivalent of a differencing scheme as used in equation 1.5 of http://oregonstate.edu/instruct/ch490/lessons/lesson11_files/image005.jpg?
From: Jerry Avins on 11 Feb 2010 15:19 Dinne wrote: > Dear all, > > I need to calculate an acceleration signal from a signal containing speed > samples. I have been looking into using FIR differentiators. Especially the > article http://www.dsprelated.com/showarticle/35.php seems interesting. > > When comparing FIR differentiators, it is probably not enough to look at > just the frequency magnitude and phase delay response. > > For example one can use a simple forward difference scheme or a more > complicated five point difference scheme. The latter will result in smaller > errors. (http://oregonstate.edu/instruct/ch490/lessons/lesson11.htm) > > In http://cnx.org/content/m28304/latest they use a filter window to smooth > the frequency response of a differentiator. I do not understand however why > this approach would be better or worse than the differentiator described in > http://www.dsprelated.com/showarticle/35.php. > > No my question is: Which other graph's and figures should one calculate to > compare the quality of a FIR differentiator? > > What would be the FIR differentiator equivalent of a differencing scheme as > used in equation 1.5 of > http://oregonstate.edu/instruct/ch490/lessons/lesson11_files/image005.jpg? When there are many ways to do a task, the chances are high that all have problems, and that different ways have different problems. Deciding which way is best for a particular application requires knowing what is important for that application. Why do you need the calculated acceleration signal? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
From: Dinne on 11 Feb 2010 16:30 > >When there are many ways to do a task, the chances are high that all >have problems, and that different ways have different problems. Deciding >which way is best for a particular application requires knowing what is >important for that application. > >Why do you need the calculated acceleration signal? > Hello, In our application we have three gyroscopes. The gyroscopes will be mounted on board of a ship. Each one is sampled at 25 Hertz. The spectrum in which we are interested has a range from 0 to 6Hz. The gyroscopes measure angular rate (roll rate, pitch rate and yaw rate). The goal is to calculate angular acceleration in real time. To do this the derivative must be calculated of the angular rate. The accelerations are used to determine if a ship experienced violent movements during its journey.
From: Dinne on 11 Feb 2010 16:39 I forgot to mention that the signals will have an oscillatory behavior as the ship will roll/pitch/yaw continuously on the waves. The mean of the signal over a large number of samples will be 0.
From: Tim Wescott on 11 Feb 2010 19:53
On Thu, 11 Feb 2010 15:30:56 -0600, Dinne wrote: >>When there are many ways to do a task, the chances are high that all >>have problems, and that different ways have different problems. Deciding >>which way is best for a particular application requires knowing what is >>important for that application. >> >>Why do you need the calculated acceleration signal? >> >> > Hello, > > In our application we have three gyroscopes. The gyroscopes will be > mounted on board of a ship. Each one is sampled at 25 Hertz. The > spectrum in which we are interested has a range from 0 to 6Hz. The > gyroscopes measure angular rate (roll rate, pitch rate and yaw rate). > The goal is to calculate angular acceleration in real time. To do this > the derivative must be calculated of the angular rate. > > The accelerations are used to determine if a ship experienced violent > movements during its journey. Then you need a filter that acts like a differentiator up to around 6Hz, and whose response tails off after that. Just where you need that response to start tailing off, and how sharply, depends heavily on the noise that you expect to get from the gyros -- if the gyros are very quiet compared to the acceleration you're trying to estimate then your best bet may be a simple back-step one-delay differentiator. If the gyros are very noisy, and if you need everything below 6Hz and nothing above it (and you don't mind _lots_ of delay), then you need something very different. To really do this right you'd want to construct a Wiener filter (or a Kalman filter if you needed the thing to spin up quickly from a power-on, but I doubt that). That may well be overkill, and it requires that you know a staggering amount of close detail about the system. Without knowing a lot more about your expected noise and your accuracy requirements, the signal you're trying to pull out of it, etc., etc., etc. I cannot say. Probably the best thing to do is to get sample gyro data from calm seas conditions and from rough seas condition, and try a few different filters out on them. If you find one that seems to be good enough -- it may well be good enough. -- www.wescottdesign.com |