Band-stop filter

In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter. A notch filter is a band-stop filter with a narrow stopband (high Q factor). In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter. A notch filter is a band-stop filter with a narrow stopband (high Q factor). Narrow notch filters (optical) are used in Raman spectroscopy, live sound reproduction (public address systems, or PA systems) and in instrument amplifiers (especially amplifiers or preamplifiers for acoustic instruments such as acoustic guitar, mandolin, bass instrument amplifier, etc.) to reduce or prevent audio feedback, while having little noticeable effect on the rest of the frequency spectrum (electronic or software filters). Other names include 'band limit filter', 'T-notch filter', 'band-elimination filter', and 'band-reject filter'. Typically, the width of the stopband is 1 to 2 decades (that is, the highest frequency attenuated is 10 to 100 times the lowest frequency attenuated). However, in the audio band, a notch filter has high and low frequencies that may be only semitones apart. Band-stop filter can be represented as a combination of low-pass and high-pass filters if the bandwidth is wide enough that the two filters do not interact too much. A more general approach is to design as a low-pass prototype filter which can then be transformed into a bandstop. The simple notch filter shown can be directly analysed. The transfer function is, H ( s ) = s 2 + ω z 2 s 2 + ω p Q s + ω p 2 {displaystyle H(s)={frac {s^{2}+omega _{z}^{2}}{s^{2}+{frac {omega _{p}}{Q}}s+omega _{p}^{2}}}} Here ω z {displaystyle omega _{z}} is zero circular frequency and ω p {displaystyle omega _{p}} is the pole circular frequency. Zero frequency is the cutoff frequency and ω p {displaystyle omega _{p}} sets the type of the notch filter: standard notch when ω z = ω p {displaystyle omega _{z}=omega _{p}} , low-pass notch ( ω z > ω p {displaystyle omega _{z}>omega _{p}} ) and high-pass notch ( ω z < ω p {displaystyle omega _{z}<omega _{p}} ) filters. Q {displaystyle Q} denotes the Q-factor.