In
signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
, a band-stop filter or band-rejection filter is a
filter that passes most
frequencies
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is e ...
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 physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy ...
).
Narrow notch filters (
optical) are used in
Raman spectroscopy
Raman spectroscopy () (named after Indian physicist C. V. Raman) is a spectroscopic technique typically used to determine vibrational modes of molecules, although rotational and other low-frequency modes of systems may also be observed. Raman ...
, live sound reproduction (
public address systems, or PA systems) and in
instrument amplifiers (especially amplifiers or
preamplifiers for acoustic instruments such as
acoustic guitar
An acoustic guitar is a musical instrument in the string family. When a string is plucked its vibration is transmitted from the bridge, resonating throughout the top of the guitar. It is also transmitted to the side and back of the instrument, ...
,
mandolin
A mandolin ( it, mandolino ; literally "small mandola") is a stringed musical instrument in the lute family and is generally plucked with a pick. It most commonly has four courses of doubled strings tuned in unison, thus giving a total of ...
,
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
Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work.
At the lowest programming level, executable code consist ...
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
Audio most commonly refers to sound, as it is transmitted in signal form. It may also refer to:
Sound
*Audio signal, an electrical representation of sound
*Audio frequency, a frequency in the audio spectrum
* Digital audio, representation of sou ...
band, a notch filter has high and low frequencies that may be only
semitones apart.
Mathematical description
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,
Here
is zero circular frequency and
is the pole circular frequency. Zero frequency is the cutoff frequency and
sets the type of the notch filter: standard notch when
, low-pass notch (
) and high-pass notch (
) filters.
denotes the Q-factor.
For standard notch filter the formulation can be rewritten as
where
is the central rejected frequency and
is the width of the rejected band.
Examples
In the audio domain
;Anti-hum filter
For countries using 60
Hz power lines:
* low frequency: 59 Hz,
* middle frequency: 60 Hz,
* high frequency: 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 the 60 Hz power line, though its higher harmonics could still be present.
For countries where power transmission is at 50 Hz, the filter would have a 49–51 Hz range.
In the radio-frequency (RF) domain
;Non-linearities of power amplifiers
When measuring the non-linearities of power amplifiers, a very narrow notch filter can be very useful to avoid the
carrier frequency
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a ...
. Use of the filter may ensure that the maximum input power of a spectrum analyser used to detect spurious content will not be exceeded.
;Wave trap
A notch filter, usually a simple
LC circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can a ...
, is used to remove a specific interfering frequency. This is a technique used with radio receivers that are so close to a transmitter that it swamps all other signals. The wave trap is used to remove or greatly reduce the signal from the nearby transmitter.
[Carr, Joseph J. (2001). ''The technician's radio receiver handbook: Wireless and telecommunication technology'', p. 282. Newnes. .]
;Software-defined radio
Most affordable
software-defined radio
Software-defined radio (SDR) is a radio communication system where components that have been traditionally implemented in analog hardware (e.g. mixers, filters, amplifiers, modulators/demodulators, detectors, etc.) are instead implemented by ...
s (SDR) on the market today suffer from limited dynamic and operating ranges. In other words, in real-world operating environments, a SDR can easily be saturated by a strong signal. In particular FM broadcast signals are very strong and nearly everywhere. These signals can prevent a SDR from processing other weak signals. FM notch filters are very useful for SDR applications and have increased in their popularity.
Optical filtering (wavelength selection)
In optics, there are several methods of filtering selected wavelengths from a source or to a detector. They rely on
scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
or destructive
interference.
Filtering by scattering and diffraction
A
diffraction grating
In optics, a diffraction grating is an optical component with a periodic structure that diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structur ...
or a
dispersive prism may be used to selectively redirect selected wavelengths of light within an optical system.
In the case of transmission gratings and prisms, polychromatic light that passes through the object will be redirected according to wavelength. A slit may then be used to select wavelengths that are desired. A reflective grating may also be utilized for the same purpose, though in this case light is reflected rather than transmitted. Filters of this design may be high-pass, band-pass, or low-pass, depending on system configuration.
Filtering by interference
When using optics with real materials, light will be attenuated at various wavelengths through interference with the medium through which the light traversed. In this sense, material selection may be utilized to selectively filter light according to the wavelengths that are minimally attenuated. To some extent, all real optical systems will suffer from this phenomenon.
Alternatively, it is also possible to use an oscillating reflecting surface to cause destructive interference with reflected light along a single optical path. This principle is the basis for a
Michelson interferometer
The Michelson interferometer is a common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson. Using a beam splitter, a light source is split into two arms. Each of those ...
.
See also
*
Parametric equalizer
References
{{Electronic filters
Linear filters
Synthesiser modules
Filter frequency response
Optical filters