>> Meh. I wanted to build a digital filter, so I read a rather excellent 
>> book on the subject. ;-)
> 
> But, you see ... you have an interest in such things.

I read Wikipedia - and discovered that it is *completely useless* for 
learning this kind of thing! But then I found a book online, and read 
that. ;-)

>> Wanna see the Z-transform?
> 
> Z transform?

Weeell... The Fourier transform comes in several different "flavours", 
but essentially you have

- The continuous Fourier transform takes a formula and turns it into a 
different formula.
- The discrete Fourier transform takes some numbers and turns them into 
some other numbers.

There is a generalisation of the [continuous] Fourier transform called 
the Laplace transform. The correspondin discrete version is called the 
Z-transform.

The Laplace transform is the trippy mumma you use for designing Infinite 
Inpulse Response filters.

See, Finite Impulse Response (FIR) filters are very easy to design, and 
very flexible, but they take quite a bit of compute power. If you want 
precise filtering (e.g., for scientific purposes) then you're going to 
use FIR.

On the other hand, Infinite Impulse Response filters use feedback to 
generate an impulse response which is effectively "infinitely long". The 
downside is that only certain impulse responses can be created by 
feedback. Oh, and that controlling feedback is damned tricky.

Enter the Laplace transform. This makes it relatively easy to figure out 
how much feedback to apply.

It just so happens that the impulse response of a perfect lowpass filter 
"nearly" matches the kinds of impulse responses that an IIR can produce. 
The net result of this is that with only a tiny amount of calculation, 
you can get pretty good results.

In other words, IIR is massively, massively faster than FIR. (It's also 
far less precise, nowhere near as flexible, and way harder to design.)

While we're on the subject, the Laplace transform turns differential 
equations into algebraic equations, making them drastically easier to 
solve. As I understand it, that's why mathematicians came up with it in 
the first place.

Jesus Christ, SOMEBODY HIRE ME!! >_<

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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