stoppband

Stoppband, also called stopband, refers to the portion of the frequency spectrum that a filter is designed to suppress or attenuate to a specified level. It is defined relative to the passband, where the signal is allowed to pass with minimal attenuation, and the transition band, the intermediate region where attenuation increases from the passband level to the stopband level. Depending on the filter type, the stoppband can lie at high frequencies (as in a low-pass filter) or at low frequencies (as in a high-pass filter); for band-pass or band-stop filters, stoppages appear around or outside the desired passband.

The stoppband is specified by edge frequencies and a required attenuation, typically given as As in decibels. The actual magnitude response |H(f)| in the stoppband must not exceed a specified level, often expressed as |H(f)| ≤ 10^(-As/20). The boundary frequencies, f_s or ω_s, define where the stopband begins, while the transition band lies between the passband edge and the stopband edge. In digital filters, frequencies are often normalized to the sampling rate or to π radians per sample.

In practice, the stoppband is a key consideration in filter design. Designers seek to meet both passband specifications (allowing desired signals with minimal distortion) and stopband specifications (suppressing unwanted components) while minimizing the transition width and the filter order. Common design methods for FIR and IIR filters include windowing, equiripple (Parks–McClellan), and optimization techniques. The concept of stoppband is central across applications such as telecommunications, audio processing, and instrumentation, where unwanted frequencies must be attenuated without compromising the wanted signal.