Luiz Carlos wrote:> So, when I look at a signal, I do my "visual FFT", observing how > it varies on time, not in frequency, because frequency are > consequence of variation in time. Discontinuities, knees, and > very high first derivatives are easy seen. > > But as Martin pointed out, the second derivative must be > continuous too. And looking more carefully, all derivatives must > be continuous. Now I'm disappointed, because my mental FFT > algorithm has a flaw! :)Hi Luiz Carlos, Consider an impulse in the time domain. Its magnitude spectrum is of course flat. Now, a step discontinuity can be seen as resulting from integrating an impulse which is the same as applying the ideal onepole lowpass filter. Therefor, a step's spectrum falls off at 6 dB/oct. And the pattern continues: an impulse in the n'th derivative has 6n dB/oct spectral falloff. (I'm aware that it's a bit handwaving to talk about "discontinuities" in the discrete-time case, but you know what I mean. ;) Why am I telling you this? I hope to at least partially fix your mental device that I have inadvertently broken. Martin
Fast response filter?
Started by ●January 15, 2004
Reply by ●January 20, 20042004-01-20
Reply by ●January 21, 20042004-01-21
"Fred Marshall" <fmarshallx@remove_the_x.acm.org> a �crit dans le message de news:LZednWzJw5Rd-5DdRVn-hA@centurytel.net...> Patrick, > > ??? Being linear phase means that it's definitely not minimum phase. I > don't think either Bob or I suggested anything different.Indeed, that's why I canceled my msg. I didn't see that you talked about the output from the minimum phase extracting algorithm...> - The reason why is because a linear phase filter has reciprocal pairs of > zeros inside and outside the unit circle.That's the thing I don't remember the proof (must be a polynomial property)> - If the linear phase filter has zeros that are complex, then they are > paired with their complex conjugates - making each complex zero instance a > quad and each real zero instance a pair. > - For minimum phase, all the zeros have to be inside the unit circle. So > the two characteristics are mutually exclusive. > - If any complex conjugate zero pair is replaced with its reciprocal, the > magnitude response is unchanged. > - If all the zeros are outside the unit circle then it's maximum phase. > - So, a linear phase filter is a combination of minimum and maximum phase.I could add : any non-minimum phase filter is a combination of minimum phase and a (maximum phase) passthrough filter.> - And, there are a multiplicity of filters (of the same order) with thesame> magnitude response that are had by moving zeros inside or outside the unit > circle. > - Note that a linear phase filter is really a cascade of a minimum phaseand> a maximum phase so that its magnitude response is like the square of thetwo> and not the same as either one. Another way to look at this is that youcan> get a minimum phase filter with "similar" magnitude response by taking the > minimum phase square root of a linear phase filter if it's designed tohave> all positive mangitude response to begin with (Schuessler). > > Fred >This is familiar to me since I made my Phd on a loudspeaker equalization and the non-minimum phase character of the system brought to me many problems to solve. The Hilbert transform was a real friend. Thank you anyway for your explanation. Patrick
Reply by ●January 21, 20042004-01-21
> Consider an impulse in the time domain. Its magnitude spectrum is of > course flat. Now, a step discontinuity can be seen as resulting from > integrating an impulse which is the same as applying the ideal > onepole lowpass filter. Therefor, a step's spectrum falls off at 6 > dB/oct. And the pattern continues: an impulse in the n'th derivative > has 6n dB/oct spectral falloff. (I'm aware that it's a bit handwaving > to talk about "discontinuities" in the discrete-time case, but you > know what I mean. ;) > > Why am I telling you this? I hope to at least partially fix your > mental device that I have inadvertently broken. > > > MartinHi Martin, I liked it. It really helps to "reconfigure my visual FFTs"! I was thinking. A signal to be bandlimited (frequency) must be periodic and vice-versa. But, (almost all) real world signals are not periodic, and therefore, they are not bandlimited. So, when we record some signal, even voice, we are losing part of its spectrum. And it doesn't matter if it's a digital or an analog record, both are bandlimited. Conclusion, nothing is perfect! Maybe I should not want to kill those people who listen to MP3. :) Luiz Carlos.
Reply by ●January 21, 20042004-01-21
In article <400bf610$0$6083$61fed72c@news.rcn.com>, Jerry Avins <jya@ieee.org> wrote:>Luiz Carlos wrote: >> ... I simply just can't see where are these high frequency >> components coming from! > >The "Argument from Disbelief" is dangerously seductive -- creationists >use it often -- but not logically sound.<ob-occasional-completely-off-topic-post> Funny that this statement would appear in an engineering forum. No engineer would send a signal without considering the response of the channel and receiver. If "Argument by xyz" has greater than X% chance of being received correctly by a particular human audience, then depending on X, its use might be considered perfectly logically sound. The global marketing based economy depends on this about as much as physicists depend on argument from mathematical construct.> What combination of sines and >cosines of various frequencies, existing throughout time, would you >need to add together to create your test waveform?Of course this makes sense in the mathematical analysis of linear time invarient systems, but that may or may not have anything to do with an intuitive picture of the real world, much of which sometimes behaves in a highly non-linear and time dependant manner. So one answer is that the frequencies are only there because of the mathematical assumptions used in the analysis, not in the real world where Luiz switched on the signal generator (or hitched a pony up to his wheeled wagon) just after lunch hour (or whatever). </ob-occasional-completely-off-topic-post> IMHO. YMMV. (and this post may have been composed by line noise...) -- Ron Nicholson rhn AT nicholson DOT com http://www.nicholson.com/rhn/ #include <canonical.disclaimer> // only my own opinions, etc.
Reply by ●January 21, 20042004-01-21
Reply by ●January 21, 20042004-01-21
Luiz Carlos wrote: ...> I was thinking. A signal to be bandlimited (frequency) must be > periodic and vice-versa. But, (almost all) real world signals are not > periodic, and therefore, they are not bandlimited. > So, when we record some signal, even voice, we are losing part of its > spectrum. And it doesn't matter if it's a digital or an analog record, > both are bandlimited. > > Conclusion, nothing is perfect! > Maybe I should not want to kill those people who listen to MP3. :) > > Luiz Carlos.Luiz, Of course nothing is perfect.* For one thing, there is always noise. When the difference between a theoretical signal and the real one we have to settle for becomes much less than that noise, then noise is the only perceptible imperfection. There can't really be an infinite- impulse-response filter, because the gizmo it's in gets turned off sooner or later. Don't lose sleep over it. Jerry ____________________ * Almost nothing. Some things are perfectly awful. -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." Barbara Smuts, U. Mich. ���������������������������������������������������������������������
Reply by ●January 21, 20042004-01-21
Ronald H. Nicholson Jr. wrote: ...> No engineer would send a signal without considering the response of > the channel and receiver. If "Argument by xyz" has greater than X% > chance of being received correctly by a particular human audience, then > depending on X, its use might be considered perfectly logically sound.Its use might be sound marketing, or propaganda, or what have you, but the logic of the argument which is what I sought to address is unsound.> The global marketing based economy depends on this about as much as > physicists depend on argument from mathematical construct.If we were better at thinking straight, that wouldn't work.>>What combination of sines and >>cosines of various frequencies, existing throughout time, would you >>need to add together to create your test waveform? > > > Of course this makes sense in the mathematical analysis of linear > time invarient systems, but that may or may not have anything to > do with an intuitive picture of the real world, much of which > sometimes behaves in a highly non-linear and time dependant manner. > > So one answer is that the frequencies are only there because of > the mathematical assumptions used in the analysis, not in the real > world where Luiz switched on the signal generator (or hitched a pony > up to his wheeled wagon) just after lunch hour (or whatever). > > </ob-occasional-completely-off-topic-post> > > IMHO. YMMV. (and this post may have been composed by line noise...)As you wrote, whatever. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●January 21, 20042004-01-21
Luiz Carlos wrote:> Oops, > > Not all periodic signal are bandlimited! > > Luiz Carlos.We knew what you meant, but try this one on for size: all real-world signals are bandlimited. Otherwise, when striking a bell, you would get radio interference, illumination, and X-rays. Math is about models. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●January 21, 20042004-01-21
"Luiz Carlos" <oen_no_spam@yahoo.com.br> wrote in message news:3fd8f66b.0401210236.77b33136@posting.google.com...> Oops, > > Not all periodic signal are bandlimited! >Luis Carlos, Nor are all bandlimited signals periodic..... Fred
Reply by ●January 21, 20042004-01-21
"Jerry Avins" <jya@ieee.org> wrote in message news:400eb4e1$0$2440$61fed72c@news.rcn.com...>......Otherwise, when striking a bell, you would get > radio interference, illumination, and X-rays.Jerry .... how in the world .... ???? Or, did you have some transformation of energy mechanism in mind that isn't obvious. Were you referring to heat -> IR -> electromagnetic radiation? Otherwise, the model generally stays focused on mechanical energy in the case of a bell and the heat is neglected. Either way bandwidth has nothing to do with it. Well .... unless there's some mechanism in going to heat / IR that somehow supports the creation of infinite bandwidths. Yeah, I know that supports the point of it being "real". But the example seems to jump from one type of energy to another without justification. I have the feeling that I'm missing something but, as one might expect, don't know what it is! Fred
