Convolution Tutorial

There's nothing intuitive about convolution. It's an arcane mathematical technique which produces blank looks from lecturers when they are quizzed about it. There's nothing intuitive about sliding two pieces of paper together.

Which is where I came in. A demonstration of the responses of systems followed by an analysis of what's going on will result in the convolution as a derived result, which is the right way of presenting it.

Thinking is not something that can be taught.

Not everyone who tries makes it as an engineer. You can be taught the skills, but you have to have the creativity to see X number of parts/tools/circuits/etc. and to be able to put them into new designs.

I've seen people trained to be an engineer who couldn't make it; they end up as checkers if they want to stay in the field.

Concepts like convolution need quite a bit of thought and different people have different things that make the light bulb go off in their head. You have found a way for you that made the light go off, and I agree that it is a good method. But , the light typically goes off after looking at the concept several different ways. My website is intended to help someone who has already had some exposure through textbooks to the various topics I present. It is intended to give one more insight that may help. Concepts like convolution and fourier series do not come without a certain dedication to learning them on the students part.

Because their parent's didn't read them "Heather has Two Mommies".

Not so. The difficulties lie with the incompetence of lecturers and authors.

Too many textbooks, and, dare I say, websites, seem to exist as an ego-trip for the author rather than as an aid to the student.

Not to mention professors, colleges, and politicians. All the same class of nitwits, now.

I disagree with you here. Ultimately, learning is up to the individual. If someone wants to learn something, then that person has the responsibility to learn it.

As far as textbooks authors are concerned, they are the real champions of learning. It is on the backs of people who took the time to write a book that all advanced learning is based. I feel that I owe all my knowledge of EE to those people who took the time to write the books. So you can sit and criticize all the bad books, I will wrestle with them and try to understand what they say. At least I have a clue with the book. Without the book I have no where to start, and I certainly am not smart enough to self derive every concept in EE.

Tell them to prove it. :)

It is when I explain it, as it was explained to me, sliding slips of paper and all. It's not just a mathematical operation, it's something you can see and feel... if your mind is so inclined.

If the lecturers think it's just math, and don't feel what's going on, I feel sorry for them... and their students.

The right way of presenting it is so that people truly understand it, not just learn how to crank the equations.

This is a graph from a program that iteratively solves a reverse convolution problem. The program derives the purple filter such that its impulse response, convolved with the distorted yellow input, produces the target white step response. This will turn a sloppy full-of-reflections sampling scope/TDR into a good one. The algorithm was designed intuitively, not analytically.

ftp://jjlarkin.lmi.net/Inv_Conv_demo.jpg

Fun to play with, too. If you get too ambitious about risetime enhancement, or want too much precision in the presence of noise, it explodes in impressive ways. This is directly related to the divide-by-zero dilemma in FFT-based inverse convolution.

This stuff is literally simple once you get the hang of it and practise a bit.

Absurd! Of course it can.

John

Engineering profs have a tendency to feel inferior to "real scientists" and apply mathematical rigor as if it were enough. It's not.

John

Or to discover every mathematical principle of import to engineering today.

Which is why bad textbooks, and bad websites, should be severely panned, especially those which start off describing convolution as an arcane never-to-be-fathomed mathematical process when in fact it is a straightforward derivation from the response of systems.

The mental processes that you followed in generating your answer above were subconscious. Your thinking mechanisms are innate from when you were born, and not something trained into you.

As I said, dogs are trained. Engineers have to think. The way to learn how to think is to do it a lot, and working with other people who already know how can vastly accelerate the process.

But like anything else, some aptitude is required. And like anything else, we pass on the skill as part of our culture.

John

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Just because you resent the language used, does not mean that=20 cognitive skills, such as scientific method, cannot be learned. The increase in skills to use such methods comes from a combination=20 of talent and dedicated practice.