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Designing the Filter
You must select four parameters to design a Chebyshev filter: (1) a high-pass
or low-pass response, (2) the cutoff frequency, (3) the percent ripple in the
passband, and (4) the number of poles. Just what is a pole? Here are two
answers. If you don't like one, maybe the other will help:
Answer 1- The Laplace transform and z-transform are mathematical ways of
breaking an impulse response into sinusoids and decaying exponentials. This
is done by expressing the system's characteristics as one complex polynomial
divided by another complex polynomial. The roots of the numerator are called
zeros, while the roots of the denominator are called poles. Since poles and
zeros can be complex numbers, it is common to say they have a "location" in
the complex plane. Elaborate systems have more poles and zeros than simple
ones. Recursive filters are designed by first selecting the location of the poles
and zeros, and then finding the appropriate recursion coefficients (or analog
components). For example, Butterworth filters have poles that lie on a circle
in the complex plane, while in a Chebyshev filter they lie on an ellipse. This
is the topic of Chapters 32 and 33.
Answer 2- Poles are containers filled with magic powder. The more poles in
a filter, the better the filter works.
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