passbandstopband

Passbandstopband is a shorthand description used to refer to the two primary regions of a filter’s frequency response: the passband and the stopband. In linear time-invariant filters, the magnitude response is designed so that frequencies in the passband pass with minimal attenuation, while frequencies in the stopband are suppressed or rejected.

Passband: The passband comprises the frequencies the filter is intended to transmit with little loss. The gain within this region is specified to stay within a prescribed tolerance of the nominal pass gain, often near 0 dB. Passband edges define where the transition to attenuation begins, and passband ripple describes allowable variation in amplitude within this region.

Stopband: The stopband contains frequencies that the filter should attenuate substantially. The required attenuation level, given in decibels (A_s), characterizes how strongly undesired frequencies must be suppressed. Stopband edges mark where the attenuation must meet or exceed the specification. Higher stopband attenuation improves suppression of interference and noise but may require higher filter order.

Transition band: The transition band lies between the passband and stopband and is the region where attenuation rises from the passband level to the stopband level. The width of the transition band, along with the overall filter order, is a key design trade-off. In digital implementations, sampling rate and discretization influence the attainable transition behavior.

Implementation and design: Filters can be analog or digital, and can be FIR or IIR. Common design methods include windowing, least-squares, and minimax (equiripple) approaches. Specifications typically specify passband ripple, stopband attenuation, and transition bandwidth. Practical considerations include phase response, numerical stability, and computational resources.

Applications: Well-controlled passbandstopband characteristics are essential in communications systems, audio and video processing, RF front-ends, and instrumentation to separate desired signals from interference and noise.