Remove a specific frequency while passing all others
In audio and biomedical signals, power line hum at 50 Hz (Europe) or 60 Hz (Americas) often corrupts recordings. A notch filter removes this interference without affecting other frequencies.
Zeros on Unit Circle: A notch filter places zeros exactly on the unit circle at the notch frequency. These zeros create infinite attenuation (in theory) at that frequency.
Poles Near Zeros: Poles are placed close to the zeros but slightly inside the unit circle. The closer the poles, the sharper (higher Q) the notch.
Q Factor: Determines the bandwidth of the notch. Higher Q = narrower notch = less effect on nearby frequencies.
Trade-off: Very high Q can cause ringing. Very low Q removes too much of the signal around the notch frequency.