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Dennis,
>> example, I recently constructed a 6-pole highpass filter that had
>> a more "desirable" (to me) temporal response to a step function.
>> The frequency response was such that it leveled off at 14 dB about
>> an octave away from the 3 dB point, stayed there for another half
>> octave or so, and then fell off further from there.
You might be interested to know that this was an all-pole filter
with no zeros, constructed by summing two all-pole filters together
in an attempt to get the overshoot of one to cancel out the lag of
the other through destructive interference.
>"Pole: Term used in the Laplace transform and z-transform. When the
>s-domain or z-domain transfer function is written as one polynomial
>divided by another polynomial, the roots of the denominator are the
>poles of the system, while the roots of the numerator are the zeros."
I think of it as: you have a ratio of two polynomials. A "zero" is
whatver value of x you must use to make the numerator equal zero.
A "pole" is a value of x that makes the ratio blow up to infinity
(denominator equals zero). A graph will look sort of like poles
sticking up out of a hillside, with zeros being holes going down to
zero.
-Alex
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