On 10/09/2010 09:38 AM, Invisible wrote:

> Next fun thing: Transforming from rectangular to polar coordinates. It's
> not as simple as you think it is.

Other fun things:

* If you place a pole and a zero on top of each other, mathematics says 
they should cancel each other out. In the real world, this doesn't work 
at all! (It's called a pole-zero cancellation, and you want to stay the 
hell away from it.)

* An IIR filter is a feedback loop. Feedback magnifies rounding errors. 
So after you design your filter, you may find that it doesn't actually 
have the frequency response it's supposed to have. (Depending on whether 
you use fixed-point or floating-point arithmetic, and at what precision.)

* The more poles a lowpass filter has, the better its frequency response 
theoretically becomes. However, more poles increases the passband gain, 
so you have to turn down the A-coefficients, while the extra poles keep 
increasing the number and magnitude of the B-coefficients. Gradually you 
end up with a filter that's less and less sensitive to its input 
(A-coefficients), and has higher and higher gain in the feedback path 
(B-coefficients). Can you spell "unstable"?

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