Convolution Tutorial

Started by December 26, 2009
```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
```
```"brent" <bulegoge@columbus.rr.com> wrote in message
>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.

```
```"brent" <bulegoge@columbus.rr.com> wrote in message
>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.

```
```"brent" <bulegoge@columbus.rr.com> wrote in message
>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.

```
```"brent" <bulegoge@columbus.rr.com> wrote in message
>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.

```
```"brent" <bulegoge@columbus.rr.com> wrote in message
>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.

```
```"brent" <bulegoge@columbus.rr.com> wrote in message
>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.

```
```On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:

> "brent" <bulegoge@columbus.rr.com> wrote in message
>>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
apprenticeship, which severely cuts down on the available candidate pool.

--
www.wescottdesign.com
```
```On 27 Des, 11:01, "invalid" <inva...@invalid.invalid> wrote:
> "brent" <buleg...@columbus.rr.com> wrote in message
>
>
> >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
```
```On 27 Des, 20:31, Tim Wescott <t...@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
```