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Filters can be designed from its pole zero plot. Following two constraints should be imposed while designing the filters.

**DESIGNING FILTER FROM POLE ZERO PLACEMENT**

Filters can be designed from its pole zero plot.
Following two constraints should be imposed while designing the filters.

1. All poles should be placed
inside the unit circle on order for the filter to be stable. However zeros can
be placed anywhere in the z plane. FIR filters are all zero filters hence they
are always stable. IIR filters are stable only when all poles of the filter are
inside unit circle.

2. All complex poles and zeros
occur in complex conjugate pairs in order for the filter coefficients to be
real.

In the design of low pass filters, the poles should
be placed near the unit circle at points corresponding to low frequencies (
near ω=0)and zeros should be placed near or on unit circle at points
corresponding to high frequencies (near ω=∏). The opposite is true for high
pass filters.

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