bandstop

A bandstop filter, also called a notch filter, is a signal processing device or algorithm that attenuates frequencies within a specified range (the stopband) while allowing frequencies outside that range to pass with minimal attenuation. It is the frequency-domain complement of a bandpass filter.

In a frequency response, a bandstop filter shows a dip or notch centered at a target frequency f0 (or angular frequency ω0). The width of the attenuated region is described by the bandwidth, BW, and the sharpness of the notch is quantified by the quality factor Q = f0/BW. Narrow notches (high Q) remove a small frequency range with little effect elsewhere, while broader notches affect a wider portion of the spectrum.

Realizations may be analog or digital. Analog implementations often use LC networks or active components to create zeros on the imaginary axis, producing a notch in the response. Digital implementations use finite impulse response (FIR) or infinite impulse response (IIR) structures. A common second-order IIR notch has a transfer function of the form H(s) = (s^2 + ω0^2) / (s^2 + (ω0/Q)s + ω0^2) in continuous time, and its discrete-time counterpart H(z) places zeros on the unit circle at z = e^{±jω0}.

Applications include removing power-line interference in biomedical signals, eliminating hum or other narrowband noise in audio and instrumentation systems, and selective spectrum shaping in communications. Design considerations involve selecting f0, BW, and the desired trade-off between attenuation, passband fidelity, and phase response. Linear-phase FIR implementations can minimize phase distortion for some applications.