Convolution Tutorial
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From: brent on 26 Dec 2009 22:39 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
From: invalid on 27 Dec 2009 05:01 "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) and not just impulses (such as when hit with a hammer). I had difficulty with Convolution for years until it was explained to me in this practical way at which point it became meaningful instead of being some arcane mathematical operation which I did not really trust. Unless you introduce the student to the practical basis of why you would want to undertake such a weird operation, then you might as well give up. Mathematical analysis should come after practical experience and not before. IMHO.
From: Tim Wescott on 27 Dec 2009 14:31 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. 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. For many systems, using convolution is a horribly indirect way to implement what should be a simple, limited-state, ordinary linear differential equation. > and not just impulses (such as when hit > with a hammer). I had difficulty with Convolution for years until it was > explained to me in this practical way at which point it became > meaningful > instead of being some arcane mathematical operation which I did not > really trust. > > Unless you introduce the student to the practical basis of why you would > want to undertake such a weird operation, then you might as well give > up. > > Mathematical analysis should come after practical experience and not > before. I do agree that mathematical analysis should be kept firmly in the context of what is real -- when I teach control systems I try to draw examples from the real world as often as possible, and I try to keep a clear distinction between the thing you're interested in and the mathematical model that you've made of it. But then, you've already wandered away from reality if you're claiming that real systems convolve their input signals with unfailing accuracy. In today's world I don't think you can ask for practical experience before theoretical knowledge, though -- with that assumption, engineering schools would only take technicians who had already been through an apprenticeship, which severely cuts down on the available candidate pool. -- www.wescottdesign.com
From: Rune Allnor on 27 Dec 2009 14:42 On 27 Des, 11:01, "invalid" <inva...(a)invalid.invalid> wrote: > "brent" <buleg...(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. Then you have a problem. Like it or not, DSP is applied maths. > 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) and not just impulses (such as when > hit with a hammer). It is an *idealized* *representation* of what happens. > I had difficulty with Convolution for years until it > was explained to me in this practical way at which point it became > meaningful Did you pay tuition fees to anyone for teaching you DSP before that? If so, you might have a law case for them not delivering what you paid them for. > instead of being some arcane mathematical operation which I did not > really trust. Do you trust that 2+2 = 4? Or that you go bankrupt if you spend more $$$ than your income can sustain? If so you will have to trust convolution. > Unless you introduce the student to the practical basis of why you would > want to undertake such a weird operation, then you might as well give up. Nope. Get new students. Abstractions and engineering are hard intellectual work. Throughout history only a slect small percentage of the population have turned out to be able to handle such concepts. If people who can not cope with these kinds of things try to learn DSP, it is *their* problem; not the subject's. > Mathematical analysis should come after practical experience and not > before. No. > IMHO. You are plain wrong. Rune
From: Rune Allnor on 27 Dec 2009 14:47
On 27 Des, 20:31, Tim Wescott <t...(a)seemywebsite.com> wrote: > In today's world I don't think you can ask for practical experience > before theoretical knowledge, though -- with that assumption, engineering > schools would only take technicians who had already been through an > apprenticeship, which severely cuts down on the available candidate pool. Norwegian engineering schools have been forced to take students educated in 'the school of life', under the pretext that people with 'life experience' have qualities that complement the academic qualifications of the intended student base. Not surprisingly, the result was that levels plumitted to the level where no one learned anything. Whe I had my engineering education, it was required that students gained a certain number of weeks experience from industry before a degree was awarded. The idea might have worked some time in pre-neolithic ancient history; by the time I went there, any job would qualify; from flipping burgers to running 45 MW furnaces. Oh well. Rune |