Stopbanddemping

Stopbanddemping (stopband attenuation) refers to the amount by which a filter suppresses signals whose frequencies lie in the stopband. In a linear time-invariant filter, the frequency response H(f) has a passband where |H(f)| is close to unity, a transition band where attenuation rises, and a stopband where |H(f)| is small. The stopbandattenuation A_s is typically specified in decibels and represents the minimum attenuation achieved for frequencies in the stopband.

In filter design, higher stopband attenuation reduces leakage of unwanted frequencies but may require longer impulse responses or more computation. Designers choose target A_p (passband ripple) and A_s, along with passband edge f_p and stopband edge f_s, to determine filter order. Common approaches include FIR design using windowing or the Parks–McClellan algorithm, and IIR designs such as Butterworth, Chebyshev, and Elliptic filters. A FIR with linear phase can achieve controlled phase response at the cost of higher order.

Measurement and application: The magnitude constraint in the stopband is |H(f)| <= 10^(-A_s/20) for f in the stop region. Stopband attenuation is critical in communications to reject adjacent channels, in sampling to prevent spectral aliasing, and in audio or image processing to suppress out-of-band noise. The transition band width and attainable A_s depend on design choice and hardware constraints.