Convolution Tutorial

Dang, I was hoping the audio was of waveforms. Should add some DSP to that so the user can hear what the heck is happening to a signal. And a stop button, because those messages are really long...

Tim

-- Deep Friar: a very philosophical monk. Website:

Very nice, Brent !

I love your tutorial method.

boB

Very nice, Brent !

I love your tutorial method.

boB

that

p

I added an audio stop button.

Regarding the DSP comment, there is another tutorial on the site that deals with the convolution of discrete signals. It would be nice to manipulate audio signals, but that is beyond what I am trying to accomplish. Thanks for the comments.

On a sunny day (Sat, 26 Dec 2009 19:38:13 -0800 (PST)) it happened brent wrote in :

Nice!

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.

I stressed that convolution should be looked at as two distinct things.

One - a mathematical operation

Two- a way in which outputs are derived from inputs in real world systems. I think you tuned out before you heard that part.

Thanks for the comments.

thanks

4 Megs? Gonna take forever on dial-up if it works at all. But the subject is of enough interest to me that i will give it a try.

Flash means I shan't be using it.

--
"Electricity is of two kinds, positive and negative. The difference
is, I presume, that one comes a little more expensive, but is more
durable; the other is a cheaper thing, but the moths get into it."
                                             (Stephen Leacock)

There's nothing arcane about it. The formal mathematical operation can be demonstrated graphically and intuitively, by, say, sliding pieces of paper past one another. And breaking a real-life waveform into a series of impulses, and superposing system impulse responses to them, is also quite intuitive. Agree that just throwing a lot of math on a whiteboard, as academics are wont to do, isn't very intuitive.

An FIR filter is a direct, easy to understand convolution machine.

The "practical experience" and the theory are best shown simultaneously.

John

A really interesting problem is inverse convolution: given input waveform A and desired waveform Y, what black-box transfer function T will convert A into Y?

Y = A ** T Given A and Y, find a decent T.

A lot of work has been done here. It's the basis of adaptive equalizers and such. The inverse convolution issue is one of the "ill-posed problems."

John

It's easy in the frequency domain...

Just because 1/0 is difficult to deal with... :-)

..

it

would

up.

Agreed. I have always learned the topic best when that was done.

Mediocre. Thanks for trying. The audio explanations need cleaned up. A couple more examples with more useful waveforms could really help. =46or example, synchronizing CDMA signals. It needs a bit different=20 approach though.

MIT was fabulous for that. Math courses and engineering, physics and chemistry courses were synchronized... you got the math JIT for when you needed it. ...Jim Thompson

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.

Coming from you, I will take the grade of "mediocre" as a compliment.

And why would any engineer under training want to see two pieces of paper sliding past one another?

What possible relevance could it be to him?

It would give her an intuitive understanding of convolution. And all linear system response is convolution.

But training? Dogs are trained. Engineers are taught to think.

John