Convolution Tutorial
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From: Jerry Avins on 28 Dec 2009 14:05 Tim Wescott wrote: > On Mon, 28 Dec 2009 11:59:52 -0500, Jerry Avins wrote: > >> steveu wrote: >>>> On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote: >>>> >>>>> "brent" <bulegoge(a)columbus.rr.com> wrote in message >>>>> news:0fd6f825-e7ad-4642- >>>> a5fe-83de8ff8f7f6(a)x18g2000vbd.googlegroups.com... >>>>>> I have created a tutorial on the convolution integral. It uses an >>>>>> interactive flash program with embedded audio files. It is located >>>>>> here: >>>>>> http://www.fourier-series.com/Convolution/index.html >>>>> You start off by saying that convolution is a mathematical operation, >>> at >>>>> which point I switched off. >>>>> >>>>> Convolution is the way that real systems in the real world (such as >>>>> pianoforte strings) >>>>> respond to stimuli that are continuous (such as a sine wave from a >>>>> loudspeaker in close proximity) >>>> Convolution is _not_ the way that real systems in the real world >>>> respond >>>> to stimuli of any sort. Convolution is just a _mathematical >>>> operation_ that _approximates_ what real systems do. Sometimes it >>>> even does it >>> well. >>> >>> Convolution *is* the way many real systems behave. Its not some arcane >>> mathematical trick. Its the direct mathematical representation of the >>> underlying physical process. How well it fits reality is generally a >>> matter of how much the system is affected by second order effects. This >>> is pretty much like any other area of science and engineering. >>> >>>> All real systems are nonlinear. The convolution operation is one way >>>> to >>>> implement a linear model of a system. Thus, the convolution operation >>>> does not model any real system with 100% accuracy. As a model, the >>>> convolution operation is only as good as the fit between its bedrock >>>> assumption of linearity and the system's actual conformity to linear >>>> behavior. >>> You must absolutely loath the entire scientific education system. >>> Almost everything is taught as if it obeys relatively simple >>> relationships, and that's pretty much always a first order >>> approximation. Often the higher order elements are so small you can >>> largely ignore them. If you want accuracy, you'd better scrap Newton's >>> laws of motion. >>> >>> If you really want to complain about people being taught about stuff >>> like its an real accurate model, look at the real villans, like how >>> capacitors are taught. The number of engineers who treat them like they >>> are linear devices is truly sad. They demand that the latest silicon >>> can do A/D conversion at high speed with >16 bits precision, and then >>> surround them with tiny surface mount capacitors who's characteristics >>> are bizarrely funky. >> I had one guy with a Ph.D. in some electrical branch of physics tell me >> that the curved line on the schematic representation of a 'lytic was a >> "mere visual embellishment". To prove that a polar capacitor was a >> contradiction in terms, he wrote out the defining equation. > > You mean the defining equation of a cap? Leaving out all the nasty non- > ideal features that real people have to deal with every day? Yes. > An electrolytic capacitor is just a really poor diode with deceptive > packaging. I know. I once made a bank of small electrolytic rectifiers* to get DC out of the poweer line. > Nothing is more useful than a practical guy with a PhD, but having a PhD > sure doesn't guarantee that practical bent. He was a good learner when he learner that there was something to learn. Being stuck with him, I assigned a technician to be his tutor. He became quite capable in a short time. Jerry _____________________________ A lead and an aluminum strip suspended by a cork in a test tube of sodium carbonate solution. 20 in series gave enough margin for 120 VRMS. -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
From: Fred Marshall on 28 Dec 2009 15:21 I'd be happy to say, as has been already said, that a mathematical treatment is a "model" and that "models" as such aren't *necessarily* complete representations of the real world. After that, it's all a matter of degree, perception, requirements, etc. isn't it? To argue that a models in general are indeed representations of the real world without qualification seems odd to me. And, to be sure, some have given qualifications. It's the unqualified assertions that aren't well justified IMHO. Now, if one can pose physical situations where it is asserted that there need be no qualifications then we can always discuss those specific cases on their own merits. Fred
From: Rick Armstrong on 28 Dec 2009 16:39 > If arguments about capacitor nonlinearities are too subtle, try doing > this with a 1000 ohm resistor, a 1 microfarad, 50V cap, then plug the > assembly into a 120V, 60Hz wall socket. > > As a thought experiment, of course. I've done that one, inadvertently. It's a real...blast! Rick
From: Rune Allnor on 28 Dec 2009 17:59 On 28 Des, 19:22, Eric Jacobsen <eric.jacob...(a)ieee.org> wrote: > On 12/28/2009 10:50 AM, Tim Wescott wrote: > > Nothing is more useful than a practical guy with a PhD, but having a PhD > > sure doesn't guarantee that practical bent. > > Practical guys with PhDs are very rare in my experience. I think in my > entire career I've met a handful that I would say "get it" from both a > practical and theoretical perspective. > > It takes a lot of one's formative years to get a PhD, and it takes a lot > of one's formative years to get good, practical experience. Agreed. > People > with PhDs are seldom put in the same positions where people get really > useful practical experience, so the sorts of circumstances where > somebody would wind up with both good practical formative experience and > a PhD are pretty rare. There is the middle way: A PhD who doesn't understand the practical aspects, but who knows that he doesn't understand. > But I have met a lot of people with PhDs who -think- they understand > practical stuff but don't (like Jerry's guy with the electrolytic cap). > Often no amount of evidence or cajoling will convince them otherwise. > Sometimes these are the guys you want to keep far, far away from your > project. The main problem with these guys is not that they lack practical skills, but that they don't realize the fact. Somebody who knows they are in deep waters might take the necessary steps to get help or assistance. There is a saying in Norwegian, "Den som tror han er ferdig utlært er ikke utlært. Han er ferdig." In my translation: "He who thinks his education has finished is not educated. He is finished." Rune
From: Eric Jacobsen on 28 Dec 2009 18:33
On 12/28/2009 3:59 PM, Rune Allnor wrote: > On 28 Des, 19:22, Eric Jacobsen<eric.jacob...(a)ieee.org> wrote: >> On 12/28/2009 10:50 AM, Tim Wescott wrote: > >>> Nothing is more useful than a practical guy with a PhD, but having a PhD >>> sure doesn't guarantee that practical bent. >> Practical guys with PhDs are very rare in my experience. I think in my >> entire career I've met a handful that I would say "get it" from both a >> practical and theoretical perspective. >> >> It takes a lot of one's formative years to get a PhD, and it takes a lot >> of one's formative years to get good, practical experience. > > Agreed. > >> People >> with PhDs are seldom put in the same positions where people get really >> useful practical experience, so the sorts of circumstances where >> somebody would wind up with both good practical formative experience and >> a PhD are pretty rare. > > There is the middle way: A PhD who doesn't understand the > practical aspects, but who knows that he doesn't understand. > >> But I have met a lot of people with PhDs who -think- they understand >> practical stuff but don't (like Jerry's guy with the electrolytic cap). >> Often no amount of evidence or cajoling will convince them otherwise. >> Sometimes these are the guys you want to keep far, far away from your >> project. > > The main problem with these guys is not that they lack > practical skills, but that they don't realize the fact. > Somebody who knows they are in deep waters might take > the necessary steps to get help or assistance. > > There is a saying in Norwegian, > > "Den som tror han er ferdig utl�rt er ikke utl�rt. > Han er ferdig." > > In my translation: > > "He who thinks his education has finished is not educated. > He is finished." > > Rune Hehe. I like that, and I agree. People (with PhDs or not) who know what they know and, more importantly, know what they don't know, are by far, IMHO, the biggest assets. The PhDs with good theoretical, analytical, and simulation skills can be invaluable, as those are critical skills to apply to many problems. Having people who know how to take the results of the theory, analysis, and sims and apply them to practical solutions is also invaluable. Having people who know the real nuts and bolts (and solder and wire) of how to build stuff that works and holds up in the real world is also invaluable. They are, far and away more often than not, different people for each role. Some people can bridge two of those three, if they're really good, but it's extremely rare that somebody can bridge all three skill sets with good authority in each. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com |