Notchfilter

A notch filter, or notch filter network, is a type of band-stop filter designed to reject a very narrow range of frequencies while leaving most other frequencies relatively unattenuated. The targeted frequency range is called the notch, center frequency, or f0, and the surrounding frequencies pass with minimal distortion. This makes notch filters useful for removing a specific unwanted tone or interference without substantially affecting the rest of the signal.

Key characteristics of a notch filter include the center frequency f0, the bandwidth Δf (or the quality factor Q = f0/Δf), and the attenuation depth within the notch. A higher Q results in a narrower notch and a sharper transition between the rejected and passed frequencies. Notch filters can also affect phase and group delay near the notch, which may be important in some applications.

Notch filters can be implemented in several ways. Analog implementations include passive networks such as the twin-T notch filter and LC-based resonant circuits, or active configurations using operational amplifiers in multi-feedback or generalized impedance converter topologies. Digital notch filters are realized through discrete-time signal processing algorithms, typically as IIR or FIR filters. A common digital notch uses a biquad structure with a transfer function designed to place poles near the unit circle at the notch frequency to achieve sharp attenuation.

Applications span audio engineering (suppression of electrical hum at 50/60 Hz), instrumentation and measurement (removal of carrier or interference tones), biomedical signal processing (elimination of line noise in ECG or EEG), and communications. Notch filtering is chosen when a precise, narrow-frequency rejection is required with minimal impact on neighboring frequencies.