Rolloffs

Rolloffs refer to how quickly a system attenuates signals outside its passband. In signal processing and communications, the term is most often applied to filters and frequency-selective systems. The rate of attenuation is usually expressed in decibels per decade (dB/decade) or per octave (dB/octave). The key concepts are the passband, where the desired signal is preserved, the stopband, where unwanted frequencies are suppressed, and the transition band, where the response changes from passband to stopband.

The roll-off rate is largely determined by filter order. A first-order (single-pole) filter typically has about 20 dB/decade of attenuation (roughly 6 dB/octave). Each additional pole adds roughly 20 dB/decade to the asymptotic slope, so a second-order filter yields about 40 dB/decade, and so on. In practice, designers must balance transition width, passband ripple, stopband attenuation, and real-world nonidealities near the cutoff frequency. The -3 dB point is a common reference for the edge of the passband, but other specifications may use different criteria for defining its limits.

Rolloff also appears in audio and telecommunication contexts beyond generic filters. In audio, “treble roll-off” describes the diminishing high-frequency output of a loudspeaker or microphone. In digital communications, the term is used with the roll-off factor of pulse-shaping filters (often raised cosine), which defines excess bandwidth. A higher roll-off factor increases spectral occupancy but can improve timing robustness, while a lower factor conserves bandwidth at the expense of timing sensitivity.