Band-pass filter

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Bandwidth measured at half-power points (gain -3 dB, [?]2/2, or about 0.707 relative to peak) on a diagram showing magnitude transfer function versus frequency for a band-pass filter. Bandwidth 2.svg
Bandwidth measured at half-power points (gain -3 dB, 2/2, or about 0.707 relative to peak) on a diagram showing magnitude transfer function versus frequency for a band-pass filter.
A medium-complexity example of a band-pass filter. Bandpass Filter.svg
A medium-complexity example of a band-pass filter.

A band-pass filter, also bandpass filter or BPF, is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.



An example of an analogue electronic band-pass filter is an RLC circuit (a resistorinductorcapacitor circuit). These filters can also be created by combining a low-pass filter with a high-pass filter. [1]

In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, image processing, and computer graphics.

RLC circuit

An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent components of this circuit, where the sequence of the components may vary from RLC.

Resistor Passive electrical component providing electrical resistance

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat, may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, or chemical activity.

Bandpass is an adjective that describes a type of filter or filtering process; it is to be distinguished from passband, which refers to the actual portion of affected spectrum. Hence, one might say "A dual bandpass filter has two passbands." A bandpass signal is a signal containing a band of frequencies not adjacent to zero frequency, such as a signal that comes out of a bandpass filter. [2]

A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenna. The passband of a receiver is the range of frequencies it can receive.

An ideal bandpass filter would have a completely flat passband (e.g. with no gain/attenuation throughout) and would completely attenuate all frequencies outside the passband. Additionally, the transition out of the passband would have brickwall characteristics.

In practice, no bandpass filter is ideal. The filter does not attenuate all frequencies outside the desired frequency range completely; in particular, there is a region just outside the intended passband where frequencies are attenuated, but not rejected. This is known as the filter roll-off, and it is usually expressed in dB of attenuation per octave or decade of frequency. Generally, the design of a filter seeks to make the roll-off as narrow as possible, thus allowing the filter to perform as close as possible to its intended design. Often, this is achieved at the expense of pass-band or stop-band ripple.

Roll-off is the steepness of a transmission function with frequency, particularly in electrical network analysis, and most especially in connection with filter circuits in the transition between a passband and a stopband. It is most typically applied to the insertion loss of the network, but can, in principle, be applied to any relevant function of frequency, and any technology, not just electronics. It is usual to measure roll-off as a function of logarithmic frequency, consequently, the units of roll-off are either decibels per decade (dB/decade), where a decade is a 10-times increase in frequency, or decibels per octave (dB/8ve), where an octave is 2-times increase in frequency.

The decibel is a unit of measurement used to express the ratio of one value of a power or field quantity to another on a logarithmic scale, the logarithmic quantity being called the power level or field level, respectively. It can be used to express a change in value or an absolute value. In the latter case, it expresses the ratio of a value to a fixed reference value; when used in this way, a suffix that indicates the reference value is often appended to the decibel symbol. For example, if the reference value is 1 volt, then the suffix is "V", and if the reference value is one milliwatt, then the suffix is "m".

In electronics, an octave is a logarithmic unit for ratios between frequencies, with one octave corresponding to a doubling of frequency. For example, the frequency one octave from 40 Hz is 80 Hz. The term is derived from the Western musical scale where an octave is a doubling in frequency. Specification in terms of octaves is therefore common in audio electronics.

The bandwidth of the filter is simply the difference between the upper and lower cutoff frequencies. The shape factor is the ratio of bandwidths measured using two different attenuation values to determine the cutoff frequency, e.g., a shape factor of 2:1 at 30/3 dB means the bandwidth measured between frequencies at 30 dB attenuation is twice that measured between frequencies at 3 dB attenuation.

Bandwidth (signal processing) difference between the upper and lower frequencies in a continuous set of frequencies

Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth. Passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum. Baseband bandwidth applies to a low-pass filter or baseband signal; the bandwidth is equal to its upper cutoff frequency.

Cutoff frequency frequency response boundary

In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced rather than passing through.

Optical band-pass filters are common in photography and theatre lighting work. These filters take the form of a transparent coloured film or sheet.

Q factor

A band-pass filter can be characterized by its Q factor. The Q-factor is the reciprocal of the fractional bandwidth. A high-Q filter will have a narrow passband and a low-Q filter will have a wide passband. These are respectively referred to as narrow-band and wide-band filters.


Bandpass filters are widely used in wireless transmitters and receivers. The main function of such a filter in a transmitter is to limit the bandwidth of the output signal to the band allocated for the transmission. This prevents the transmitter from interfering with other stations. In a receiver, a bandpass filter allows signals within a selected range of frequencies to be heard or decoded, while preventing signals at unwanted frequencies from getting through. A bandpass filter also optimizes the signal-to-noise ratio and sensitivity of a receiver.

In both transmitting and receiving applications, well-designed bandpass filters, having the optimum bandwidth for the mode and speed of communication being used, maximize the number of signal transmitters that can exist in a system, while minimizing the interference or competition among signals.

Outside of electronics and signal processing, one example of the use of band-pass filters is in the atmospheric sciences. It is common to band-pass filter recent meteorological data with a period range of, for example, 3 to 10 days, so that only cyclones remain as fluctuations in the data fields.

Loudspeaker enclosures

Compound or band-pass

Compound or 4th order band-pass enclosure Bandpass enclosure.gif
Compound or 4th order band-pass enclosure

A 4th order electrical bandpass filter can be simulated by a vented box in which the contribution from the rear face of the driver cone is trapped in a sealed box, and the radiation from the front surface of the cone is into a ported chamber. This modifies the resonance of the driver. In its simplest form a compound enclosure has two chambers. The dividing wall between the chambers holds the driver; typically only one chamber is ported.

If the enclosure on each side of the woofer has a port in it then the enclosure yields a 6th order band-pass response. These are considerably harder to design and tend to be very sensitive to driver characteristics. As in other reflex enclosures, the ports may generally be replaced by passive radiators if desired.

An eighth order bandpass box is another variation which also has a narrow frequency range. They are often used to achieve sound pressure levels in which case a bass tone of a specific frequency would be used versus anything musical. They are complicated to build and must be done quite precisely in order to perform nearly as intended. [3]

Other fields

In neuroscience, visual cortical simple cells were first shown by David Hubel and Torsten Wiesel to have response properties that resemble Gabor filters, which are band-pass. [4]

In astronomy, band-pass filters are used to allow only a single portion of the light spectrum into an instrument. Band-pass filters can help with finding where stars lie on the main sequence, identifying redshifts, and many other applications.

See also

Related Research Articles

Superheterodyne receiver radio receiver; uses frequency mixing to convert a received signal to a fixed intermediate frequency which can be more conveniently processed than the original carrier frequency;virtually all modern radio receivers use the superheterodyne principle

A superheterodyne receiver, often shortened to superhet, is a type of radio receiver that uses frequency mixing to convert a received signal to a fixed intermediate frequency (IF) which can be more conveniently processed than the original carrier frequency. It was invented by US engineer Edwin Armstrong in 1918 during World War I. Virtually all modern radio receivers use the superheterodyne principle.

Baseband signal that has a very narrow frequency range near zero

Baseband is a signal that has a near-zero frequency range, i.e. a spectral magnitude that is nonzero only for frequencies in the vicinity of the origin and negligible elsewhere. In telecommunications and signal processing, baseband signals are transmitted without modulation, that is, without any shift in the range of frequencies of the signal. Baseband has a low-frequency—contained within the bandwidth frequency close to 0 hertz up to a higher cut-off frequency. Baseband can be synonymous with lowpass or non-modulated, and is differentiated from passband, bandpass, carrier-modulated, intermediate frequency, or radio frequency (RF).

A duplexer is an electronic device that allows bi-directional (duplex) communication over a single path. In radar and radio communications systems, it isolates the receiver from the transmitter while permitting them to share a common antenna. Most radio repeater systems include a duplexer. Duplexers can be based on frequency, polarization, or timing.


A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level. Depending on application, the required attenuation within the stopband may typically be a value between 20 and 120 dB higher than the nominal passband attenuation, which often is 0 dB.

Spectrum analyzer

A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that a spectrum analyzer measures is electrical; however, spectral compositions of other signals, such as acoustic pressure waves and optical light waves, can be considered through the use of an appropriate transducer. Optical spectrum analyzers also exist, which use direct optical techniques such as a monochromator to make measurements.

Audio filter

An audio filter is a frequency dependent amplifier circuit, working in the audio frequency range, 0 Hz to beyond 20 kHz. Audio filters can amplify (boost), pass or attenuate (cut) some frequency ranges. Many types of filters exist for different audio applications including hi-fi stereo systems, musical synthesizers, sound effects, sound reinforcement systems, instrument amplifiers and virtual reality systems.

Band-stop filter filter that passes signals outside a certain frequency range, and attenuates signals within that range

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.

Active filter active filter

An active filter is a type of analog circuit implementing an electronic filter using active components, typically an amplifier. Amplifiers included in a filter design can be used to improve the cost, performance and predictability of a filter.

Radio receiver radio device for receiving radio waves and converting them to a useful signal

In radio communications, a radio receiver, also known as a receiver, wireless or simply radio is an electronic device that receives radio waves and converts the information carried by them to a usable form. It is used with an antenna. The antenna intercepts radio waves and converts them to tiny alternating currents which are applied to the receiver, and the receiver extracts the desired information. The receiver uses electronic filters to separate the desired radio frequency signal from all the other signals picked up by the antenna, an electronic amplifier to increase the power of the signal for further processing, and finally recovers the desired information through demodulation.

Voltage-controlled filter

A voltage-controlled filter (VCF) is a processor, a filter whose operating characteristics can be applied to control inputs. It can be considered to be a frequency-dependent amplifier. Although popularly known for their use in analogue music synthesizers, in general, they have other applications in military and industrial electronics.

Optical filter device that selectively transmits light of certain wavelengths

An optical filter is a device that selectively transmits light of different wavelengths, usually implemented as a glass plane or plastic device in the optical path, which are either dyed in the bulk or have interference coatings. The optical properties of filters are completely described by their frequency response, which specifies how the magnitude and phase of each frequency component of an incoming signal is modified by the filter.


A diplexer is a passive device that implements frequency-domain multiplexing. Two ports are multiplexed onto a third port. The signals on ports L and H occupy disjoint frequency bands. Consequently, the signals on L and H can coexist on port S without interfering with each other.

Transition band

The transition band, also called the skirt, is a range of frequencies that allows a transition between a passband and a stopband of a signal processing filter. The transition band is defined by a passband and a stopband cutoff frequency or corner frequency.


A preselector is a name for an electronic device that connects between a radio antenna and a radio receiver. The preselector is a band-pass filter that blocks troublesome out-of-tune frequencies from passing through from the antenna into the radio receiver that otherwise would be directly connected to the antenna.

Prototype filter

Prototype filters are electronic filter designs that are used as a template to produce a modified filter design for a particular application. They are an example of a nondimensionalised design from which the desired filter can be scaled or transformed. They are most often seen in regard to electronic filters and especially linear analogue passive filters. However, in principle, the method can be applied to any kind of linear filter or signal processing, including mechanical, acoustic and optical filters.

Equalization (audio)

Equalization or equalisation is the process of adjusting the balance between frequency components within an electronic signal. The most well known use of equalization is in sound recording and reproduction but there are many other applications in electronics and telecommunications. The circuit or equipment used to achieve equalization is called an equalizer. These devices strengthen (boost) or weaken (cut) the energy of specific frequency bands or "frequency ranges".

Staggered tuning is a technique used in the design of multi-stage tuned amplifiers whereby each stage is tuned to a slightly different frequency. In comparison to synchronous tuning it produces a wider bandwidth at the expense of reduced gain. It also produces a sharper transition from the passband to the stopband. Both staggered tuning and synchronous tuning circuits are easier to tune and manufacture than many other filter types.


  1. E. R. Kanasewich (1981). Time Sequence Analysis in Geophysics. University of Alberta. p. 260. ISBN   0-88864-074-9.
  2. Belle A. Shenoi (2006). Introduction to digital signal processing and filter design. John Wiley and Sons. p. 120. ISBN   978-0-471-46482-2.
  4. Norman Stuart Sutherland (1979). Tutorial Essays in Psychology. Lawrence Erlbaum Associates. p. 68. ISBN   0-470-26652-X.

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