Hi, I have measured the impulse response of a plant using an MLS sequence. I now have a nice 1.3ms (130k points!) long impulse response, for which I can take the FFT and see the frequency response. The impulse response vanishes to almost zero after about 1024 samples. In fact, if I simply truncate it to 1024 samples, I get an identical frequency response. However, if I start truncating to less than 1024 samples, I do see artifacts, so I guess windowing the impulse response would be better. How are windows specified in this case? It definitely can't be to generate say a 512 points hanning window and weighting the first 512 points of my impulse response with it. This would be attenuating most of the important information! I guess the window should only be applied to the 'tail' of my impulse response, whereas the beginning would be unity. Is there a standard way to do this and specify it? Thanks!

# Truncating a measured impulse response

Started by ●December 15, 2011

Reply by ●December 15, 20112011-12-15

On 15 Des, 15:05, "gretzteam" <gretzteam@n_o_s_p_a_m.yahoo.com> wrote:> Hi, > I have measured the impulse response of a plant using an MLS sequence. I > now have a nice 1.3ms (130k points!) long impulse response, for which I can > take the FFT and see the frequency response.Yes, you *can*. But do you *need* to?> The impulse response vanishes to almost zero after about 1024 samples. In > fact, if I simply truncate it to 1024 samples, I get an identical frequency > response. However, if I start truncating to less than 1024 samples, I do > see artifacts, so I guess windowing the impulse response would be better.No. If you have N significant data points, you *don't* truncate to less than N points. No amount of windowing will correct for missing data points.> How are windows specified in this case? It definitely can't be to generate > say a 512 points hanning window and weighting the first 512 points of my > impulse response with it. This would be attenuating most of the important > information!Why do you want to window? What are you attempting to achieve? If the IP is the goal, why mess around in frequency domain? What, if anything, do you attempt to achieve by the DFT? Answering that question first, will go a long way to find out what, if any, window to apply.> I guess the window should only be applied to the 'tail' of my impulse > response, whereas the beginning would be unity. > > Is there a standard way to do this and specify it?Do you attempt to meet a standard spec? If so, you need to look up that spec and see what to do. Rune

Reply by ●December 15, 20112011-12-15

> >No. If you have N significant data points, >you *don't* truncate to less than N points. >No amount of windowing will correct for >missing data points.Very true. Thanks making it obvious!> >Why do you want to window? What are you attempting >to achieve? If the IP is the goal, why mess around >in frequency domain? > >What, if anything, do you attempt to achieve by >the DFT? Answering that question first, will go >a long way to find out what, if any, window to >apply.Well I guess I'm chasing two things at the same time, both having different requirements: -First I want to get a good frequency domain representation so I can play with classical control design and get a controller working. This way I also get a good feel for the plant, and learn more about control design. I guess what you are saying is that for this step, I could simple take the FFT of the whole data set... -Second I would like to come up with a parametric model for the plant and see what I can achieve with the state-space 'modern' control design, while learning about them at the same time. Dave

Reply by ●December 15, 20112011-12-15

try a raised-cosine window that fades only the last samples smoothly to zero. Then widen it, until the error at high frequencies is tolerable. This is just "a" possible solution, not "the" best one. If you need a finite-length impulse response that accurately models the frequency response with best accuracy in some defined frequency region(s), you can use this program: http://www.dsprelated.com/showcode/210.php Relevant sections: demo("componentmodel") and demo("componentmodel2"). As nominal frequency response, use the FFT of the "long" impulse response. This should give better results for a given IR length than windowing, but most likely it's "overkill".

Reply by ●December 15, 20112011-12-15

>> First I want to get a good frequency domain representationwell, for that I see no need to truncate the impulse response in the first place. Simply record as many samples as you like, and use FFT. The more samples you put in (including artificial zero-padding), the smaller the frequency spacing of the result. 100M points is no big deal on a modern PC, and the length does NOT need to be a power of two. The FFT output is the frequency response, as in a Bode plot (Matlab's "unwrap" comes in handy for the phase). Interpolate as needed.

Reply by ●December 15, 20112011-12-15

On Thu, 15 Dec 2011 08:29:20 -0600, gretzteam wrote:>>No. If you have N significant data points, you *don't* truncate to less >>than N points. No amount of windowing will correct for missing data >>points. > > Very true. Thanks making it obvious! > > >>Why do you want to window? What are you attempting to achieve? If the IP >>is the goal, why mess around in frequency domain? >> >>What, if anything, do you attempt to achieve by the DFT? Answering that >>question first, will go a long way to find out what, if any, window to >>apply. > > Well I guess I'm chasing two things at the same time, both having > different requirements: > > -First I want to get a good frequency domain representation so I can > play with classical control design and get a controller working. This > way I also get a good feel for the plant, and learn more about control > design. I guess what you are saying is that for this step, I could > simple take the FFT of the whole data set... > > -Second I would like to come up with a parametric model for the plant > and see what I can achieve with the state-space 'modern' control design, > while learning about them at the same time.I doubt that taking the FFT of the impulse response will give you a really good frequency-domain representation: you'll end up with lots of good detail where the plant response happens to be strong, and not-so- good detail where the plant response is low. If you then want a nice quick loop that closes at a significantly higher frequency than the plant's natural bandwidth, you'll find that information about phase shifts &c. was swamped out by noise in your initial measurement, and your system design won't 'go'. Do frequency sweeps. It gets the data you need, and insures that you have the detail where you need it. The data that you've collected will be OK for getting the parametric information, but the same comments as to lack of detail at the frequencies where you want to close the loop still applies. Getting a measurement of the plant response to random data with a good high- frequency content will help. -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com

Reply by ●December 15, 20112011-12-15

On Dec 15, 6:05�am, "gretzteam" <gretzteam@n_o_s_p_a_m.yahoo.com> wrote:> Hi, > I have measured the impulse response of a plant using an MLS sequence. I > now have a nice 1.3ms (130k points!) long impulse response, for which I can > take the FFT and see the frequency response. >... > How are windows specified in this case? It definitely can't be to generate > say a 512 points hanning window and weighting the first 512 points of my > impulse response with it. This would be attenuating most of the important > information! > I guess the window should only be applied to the 'tail' of my impulse > response, whereas the beginning would be unity. > > Is there a standard way to do this and specify it? > > Thanks!When analyzing impulse responses it is common to use the exponential window or windows constructed from half a conventional window response. If the signal outside the strong impulse response has a low noise level, you may find the rectangular window satisfactory. For the exponential window and a discussion of the potential results of impulse windowing see: http://164.125.49.61/old/data/research/International_Paper/%EA%B5%AD%EC%A0%9C%ED%95%99%EC%88%A0%EC%A7%80_0054.pdf Dale B. Dalrymple

Reply by ●December 16, 20112011-12-16

> >When analyzing impulse responses it is common to use the exponential >window or windows constructed from half a conventional window >response. If the signal outside the strong impulse response has a low >noise level, you may find the rectangular window satisfactory. > >For the exponential window and a discussion of the potential results >of impulse windowing see: >http://164.125.49.61/old/data/research/International_Paper/%EA%B5%AD%EC%A0%= >9C%ED%95%99%EC%88%A0%EC%A7%80_0054.pdf > >Dale B. Dalrymple >Hi, The link to this paper doesn't work. Do you have the title so I can google for it? Tim: I went back to the lab and re-measured everything using an exponential sine sweep, and with a long set of discrete frequency. I didn't really see any *visible* difference in the exponential sweep and MLS, but I haven't analyzed the data yet. The data coming from the tons of discrete frequency is similar too, but it seems like I would need a lot more points to really see what is going on with the phase - the unwrapping part isn't so obvious. Thanks! Dave

Reply by ●December 16, 20112011-12-16

On Dec 16, 4:32�am, "gretzteam" <gretzteam@n_o_s_p_a_m.yahoo.com> wrote:> >For the exponential window and a discussion of the potential results > >of impulse windowing see: > >http://164.125.49.61/old/data/research/International_Paper/%EA%B5%AD%... > >9C%ED%95%99%EC%88%A0%EC%A7%80_0054.pdf > > >Dale B. Dalrymple > > Hi, > The link to this paper doesn't work. Do you have the title so I can google > for it? >The link just worked for me with Firefox. Be sure your browser uses the whole link, cut and paste if necessary. Unbiased expression of FRF with exponential window function in impact hammer testing Se Jin Ahn, Weui Bong Jeong*, Wan Suk Yoo Journal of Sound and Vibration 277 (2004) 931�941 Dale B. Dalrymple