rolloff

Rolloff (or roll-off) is a term used in signal processing and related fields to describe how quickly a system's frequency response attenuates outside its passband or near a transition region. It characterizes the slope of the response as frequency moves away from the frequencies that are passed with minimal attenuation.

In filters, rolloff is typically specified as the slope of the stopband, expressed in decibels per decade or decibels per octave. A first-order low-pass filter has roughly -20 dB per decade (-6 dB per octave) of attenuation beyond the cutoff, while higher-order filters achieve steeper rolloffs. The exact shape depends on the filter type (e.g., Butterworth, Chebyshev) and order, and is often depicted in a Bode plot.

In communications and signal processing, rolloff also describes the bandwidth expansion associated with pulse shaping. The raised-cosine filter includes a roll-off factor β between 0 and 1 that sets the width of the transition band. With symbol rate Rs, the occupied bandwidth is approximately (1+β)Rs/2; β=0 yields the minimum Nyquist bandwidth, while higher β increases the required bandwidth but improves time-domain behavior and reduces intersymbol interference.

Outside electronic filters, rolloff appears in acoustics and optics to describe how a system's response diminishes at the high-frequency edge, such as speaker treble rolloff or optical filter skirts. It is a general descriptor of transition sharpness rather than a fixed measurement, and the specific meaning is context-dependent.