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A new pole-zero calculator
An update of the old Java-based pole-zero placement applet—visit that page for tips on pole-zero locations for standard biquads. The main additions are input fields for precision pole-zero placement, and an option to display the response with a log frequency scale.
The basic idea is that poles blow, zeros suck. Think of poles as controlling a frequency-dependent feedback or resonance—the impulse response of a pole inside the unit circle decays, while one outside is like runaway feedback (think of a mic feeding back into a loudspeaker). A pole on the unit circle gives a sustained oscillation (but watch out for numerical errors—keep your poles inside the unit circle, typically). Zeros absorb a particular frequency; when on the unit circle, they absorb the corresponding frequency completely.
So, poles push the frequency response up around their corresponding frequency, and zeros pull down around theirs. Keep in mind that the frequency response graph is normalized, just as the filter coefficients are. So, while a pole pushes up the response, it appears as though all other frequencies are being pushed down instead. Of course, normalization is important in practical application, but be aware of it when visualizing how poles and zeros interact.