Designing Filter From Pole Zero Placement

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.