Band-pass filter

"Bandpass" redirects here. For other uses, seeBandpass (disambiguation).

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.

Aband-pass filterorbandpass filter(BPF) is a device that passesfrequencieswithin a certain range and rejects (attenuates) frequencies outside that range. It's the opposite of aband-stop filter.

Description

In electronics andsignal processing,afilteris usually atwo-portcircuitor device which removes frequency components of asignal(an alternating voltage or current). A band-pass filter allows through components in a specified band of frequencies, called itspassbandbut blocks components with frequencies above or below this band. This contrasts with ahigh-pass filter,which allows through components with frequencies above a specific frequency, and alow-pass filter,which allows through components with frequencies below a specific frequency. Indigital signal processing,in which signals represented by digital numbers are processed by computer programs, a band-pass filter is acomputer algorithmthat performs the same function. The term band-pass filter is also used foroptical filters,sheets of colored material which allow through a specific band of light frequencies, commonly used in photography and theatre lighting, andacoustic filterswhich allow throughsound wavesof a specific band of frequencies.

An example of ananalogueelectronic band-passfilteris anRLC circuit(aresistor–inductor–capacitorcircuit). These filters can also be created by combining alow-pass filterwith ahigh-pass filter.

Abandpass signalis a signal containing a band of frequencies not adjacent to zero frequency, such as a signal that comes out of a bandpass filter.

An ideal bandpass filter would have a completely flat passband: all frequencies within the passband would be passed to the output without amplification or attenuation, and would completely attenuate all frequencies outside the passband.

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 filterroll-off,and it is usually expressed indBof attenuation peroctaveordecadeof 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-bandripple.

Thebandwidthof the filter is simply the difference between the upper and lowercutoff 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.

Q factor

A band-pass filter can be characterized by itsQfactor.TheQ-factor is thereciprocalof thefractional bandwidth.A high-Qfilter will have a narrow passband and a low-Qfilter will have a wide passband. These are respectively referred to asnarrow-bandandwide-bandfilters.

Applications

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. Signals at frequencies outside the band which the receiver is tuned at, can either saturate or damage the receiver. Additionally they can create unwanted mixing products that fall in band and interfere with the signal of interest. Wideband receivers are particularly susceptible to such interference. 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 theatmospheric sciences.It is common to band-pass filter recent meteorological data with aperiodrange of, for example, 3 to 10 days, so that onlycyclonesremain as fluctuations in the data fields.

Loudspeaker enclosures

Compound or band-pass

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 insound pressure levelcompetitions, 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.

Economics

Bandpass filters can also be used outside of engineering-related disciplines. A leading example is the use of bandpass filters to extract the business cycle component in economic time series. This reveals more clearly the expansions and contractions in economic activity that dominate the lives of the public and the performance of diverse firms, and therefore is of interest to a wide audience of economists and policy-makers, among others.

Economic data usually has quite different statistical properties than data in say, electrical engineering. It is very common for a researcher to directly carry over traditional methods such as the "ideal" filter, which has a perfectly sharp gain function in the frequency domain. However, in doing so, substantial problems can arise that can cause distortions and make the filter output extremely misleading. As a poignant and simple case, the use of an "ideal" filter on white noise (which could represent for example stock price changes) creates a false cycle. The use of the nomenclature "ideal" implicitly involves a greatly fallacious assumption except on scarce occasions. Nevertheless, the use of the "ideal" filter remains common despite its limitations.

Fortunately, band-pass filters are available that steer clear of such errors, adapt to the data series at hand, and yield more accurate assessments of the business cycle fluctuations in major economic series like Real GDP, Investment, and Consumption - as well as their sub-components. An early work, published in the Review of Economics and Statistics in 2003, more effectively handles the kind of data (stochastic rather than deterministic) arising in macroeconomics. In this paper entitled "General Model-Based Filters for Extracting Trends and Cycles in Economic Time Series", Andrew Harvey and Thomas Trimbur develop a class of adaptive band pass filters. These have been successfully applied in various situations involving business cycle movements in myriad nations in the international economy.

4G and 5G wireless communications

Band pass filters can be implemented in4Gand5Gwireless communication systems.Hussaini et al.(2015) stated that, in the application ofwireless communication,radio frequency noiseis a major concern.In the current development of5Gtechnology, planer band pass filters are used to suppressRF noisesand removing unwantedsignals.

Combine, hairpin, parallel-coupled line, step impedance and stub impedance are the designs of experimenting the band pass filter to achieve lowinsertion losswith a compact size.The necessity of adopting asymmetric frequency response is in behalf of reducing the number ofresonators,insertion loss,size and cost ofcircuitproduction.

4-pole cross-coupled band pass filter is designed by Hussaini et al.(2015).This band pass filter is designed to cover the 2.5-2.6 GHz and 3.4-3.7 GHzspectrumfor the4Gand5Gwireless communication applications respectively. It is developed and extended from 3-pole single-band band pass filter, where an additionalresonatoris applied to a 3-pole single-band band pass filter. The advanced band pass filter has a compact size with a simple structure, which is convenient for implementation. Moreover, thestop bandrejection and selectivity present a good performance inRF noisesuppression.Insertion lossis very low when covering the 4G and 5Gspectrum,while providing goodreturn lossandgroup delay.

Energy scavengers

Energy scavengers are devices that search for energy from the environment efficiently. Band pass filters can be implemented to energy scavengers by converting energy generated from vibration into electric energy. The band pass filter designed by Shahruz (2005), is an ensemble of cantilever beams,which is called the beam-mass system. Ensemble of beam-mass systems can be transformed into a band pass filter when appropriate dimensions of beams and masses are chosen. Although the process of designing a mechanical band pass filter is advanced, further study and work are still required to design more flexible band pass filters to suit large frequency intervals. This mechanical band pass filter could be used on vibration sources with distinct peak-power frequencies.

Other fields

Inneuroscience,visual corticalsimple cellswere first shown byDavid HubelandTorsten Wieselto have response properties that resembleGabor filters,which are band-pass.

Inastronomy,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 themain sequence,identifyingredshifts,and many other applications.

See also

• Atomic line filter
• Audio crossover
• Difference of Gaussians
• Sallen–Key topology

External links

• Media related toBandpass filtersat Wikimedia Commons