Notch filter

A generic ideal band-stop filter, showing both positive and negative angular frequencies

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). Notch filters are used in live sound reproduction (Public Address systems, also known as PA systems) and in instrument amplifier (especially amplifiers or preamplifiers for acoustic instruments such as acoustic guitar, mandolin, bass instrument amplifier, etc.) to reduce or prevent feedback, while having little noticeable effect on the rest of the frequency spectrum. Other names include 'band limit filter', 'T-notch filter', 'band-elimination filter', and 'band-reject filter'.
Typically, the width of the stopband is less than 1 to 2 decades (that is, the highest frequency attenuated is less than 10 to 100 times the lowest frequency attenuated). In the audio band, a notch filter uses high and low frequencies that may be only semitones apart.
Audio example 1: Anti-hum filter

• Low Freq: 59 Hz
• High Freq: 61 Hz

This means that the filter passes all frequencies, except for the range of 59–61 Hz. This would be used to filter out the mains hum from a 60 Hz power line, though its higher harmonics could still be present. The common European version of the filter would have a 49–51 Hz range.
Audio example 2: Anti-presence filter

• Low Freq: 1 kHz
• High Freq: 4 kHz

RF example 1: Non-linearities of power amplifiers For instance, when measuring non-linearities of power amplifiers a very narrow notch filter could be very useful to avoid the carrier so maximum input power of e.g. a spectrum analyser used to detect spurious content will not be exceeded.