# Category: Linear filters

Soft sensor
Soft sensor or virtual sensor is a common name for software where several measurements are processed together. Commonly soft sensors are based on control theory and also receive the name of state obse
Sallen–Key topology
The Sallen–Key topology is an electronic filter topology used to implement second-order active filters that is particularly valued for its simplicity. It is a degenerate form of a voltage-controlled v
Bridged T delay equaliser
The bridged-T delay equaliser is an electrical all-pass filter circuit utilising bridged-T topology whose purpose is to insert an (ideally) constant delay at all frequencies in the signal path. It is
Filter bank
In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the origi
Lattice network
A symmetrical lattice is a two-port electrical wave filter in which diagonally-crossed shunt elements are present – a configuration which sets it apart from ladder networks. The component arrangement
Low-pass filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency
Ensemble Kalman filter
The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnK
Composite image filter
A composite image filter is an electronic filter consisting of multiple image filter sections of two or more different types. The image method of filter design determines the properties of filter sect
Top-hat filter
The name Top-hat filter refers to several or Fourier space filtering techniques (not to be confused with the top-hat transform). The name top-hat originates from the shape of the filter, which is a re
Band-pass filter
A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.
Butterworth filter
The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude fil
Smoothing problem (stochastic processes)
The smoothing problem (not to be confused with smoothing in statistics, image processing and other contexts) is the problem of estimating an unknown probability density function recursively over time
Log Gabor filter
In signal processing it is useful to simultaneously analyze the space and frequency characteristics of a signal. While the Fourier transform gives the frequency information of the signal, it is not lo
Equalization (audio)
Equalization, or simply EQ, in sound recording and reproduction is the process of adjusting the volume of different frequency bands within an audio signal. The circuit or equipment used to achieve thi
MPX filter
MPX filter is a function found in analogue stereo FM broadcasting and equipment, FM tuners and cassette decks. An MPX filter is, at least, a notch filter blocking the 19 kHz pilot tone, and possibly h
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
Moving horizon estimation
Moving horizon estimation (MHE) is an optimization approach that uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates o
Transmission zeroes
A transmission zero is a frequency at which the transfer function of a linear two-port network has zero transmission. Transmission zeroes at zero frequency and infinite frequency may be found in high-
Gyrator
A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor
State variable filter
A state variable filter is a type of active filter in electronic circuits. It consists of one or more integrators, connected in some feedback configuration. It is essentially used when precise Q facto
Frequency dependent negative resistor
A frequency dependent negative resistor (FDNR) is a circuit element that exhibits a purely real negative resistance -1/(ω2kC) that decreases in magnitude at a rate of -40 dB per decade. The element is
All-pass filter
An all-pass filter is a signal processing filter that passes all frequencies equally in gain, but changes the phase relationship among various frequencies. Most types of filter reduce the amplitude (i
Analog sampled filter
An analog sampled filter an electronic filter that is a hybrid between an analog and a digital filter. The input is an analog signal, and usually stored in capacitors. The time domain is discrete, how
High-pass filter
A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. Th
Reconstruction filter
In a mixed-signal system (analog and digital), a reconstruction filter, sometimes called an anti-imaging filter, is used to construct a smooth analog signal from a digital input, as in the case of a d
Fraser Filter
A Fraser Filter, named after Douglas Fraser, is typically used in geophysics when displaying VLF data. It is effectively the first derivative of the data. If represents the collected data then is the
Linear filter
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in
Mechanical filter
A mechanical filter is a signal processing filter usually used in place of an electronic filter at radio frequencies. Its purpose is the same as that of a normal electronic filter: to pass a range of
Recursive Bayesian estimation
In probability theory, statistics, and machine learning, recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density
A Linkwitz–Riley (L-R) filter is an infinite impulse response filter used in Linkwitz–Riley audio crossovers, named after its inventors Siegfried Linkwitz and . This filter type was originally describ
A polyphase quadrature filter, or PQF, is a filter bank which splits an input signal into a given number N (mostly a power of 2) of equidistant sub-bands. These sub-bands are subsampled by a factor of
Quarter-wave impedance transformer
A quarter-wave impedance transformer, often written as λ/4 impedance transformer, is a transmission line or waveguide used in electrical engineering of length one-quarter wavelength (λ), terminated wi
Leapfrog filter
A leapfrog filter is a type of active circuit electronic filter that simulates a passive electronic ladder filter. Other names for this type of filter are active-ladder or multiple feedback filter. Th
Optimum "L" filter
The Optimum "L" filter (also known as a Legendre–Papoulis filter) was proposed by Athanasios Papoulis in 1958. It has the maximum roll off rate for a given filter order while maintaining a monotonic f
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 s
Analogue filter
Analogue filters are a basic building block of signal processing much used in electronics. Amongst their many applications are the separation of an audio signal before application to bass, mid-range,
Raised-cosine filter
The raised-cosine filter is a filter frequently used for pulse-shaping in digital modulation due to its ability to minimise intersymbol interference (ISI). Its name stems from the fact that the non-ze
Chebyshev filter
Chebyshev filters are analog or digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple (type I) or stopband ripple (type II). Chebyshev filters have the
Achieser–Zolotarev filter
Achieser–Zolotarev filter, or just Zolotarev filter is a class of signal processing filter based on Zolotarev polynomials. Achieser is spelled as "Akhiezer" in some sources. The filter response is sim
Elliptic filter
An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a signal processing filter with equalized ripple (equiripple) behavior
Crystal filter
A crystal filter allows some frequencies to 'pass' through an electrical circuit while attenuating undesired frequencies. An electronic filter can use quartz crystals as resonator components of a filt
Covariance intersection
Covariance intersection is an algorithm for combining two or more estimates of state variables in a Kalman filter when the correlation between them is unknown.
Gaussian filter
In electronics and signal processing mainly in digital signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian
Fast Kalman filter
The fast Kalman filter (FKF), devised by Antti Lange (born 1941), is an extension of the Helmert–Wolf blocking (HWB) method from geodesy to safety-critical real-time applications of Kalman filtering (
Anti-aliasing filter
An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theore
Bartlett's bisection theorem
Bartlett's bisection theorem is an electrical theorem in network analysis attributed to Albert Charles Bartlett. The theorem shows that any symmetrical two-port network can be transformed into a latti
Image filter end terminations
Filters designed using the image impedance methodology suffer from a peculiar flaw in the theory. The predicted characteristics of the filter are calculated assuming that the filter is terminated with
Lattice delay network
Lattice delay networks are an important subgroup of lattice networks. They are all-pass filters, so they have a flat amplitude response, but a phase response which varies linearly (or almost linearly)
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,
Gabor filter
In image processing, a Gabor filter, named after Dennis Gabor, is a linear filter used for texture analysis, which essentially means that it analyzes whether there is any specific frequency content in
Lattice phase equaliser
A lattice phase equaliser or lattice filter is an example of an all-pass filter. That is, the attenuation of the filter is constant at all frequencies but the relative phase between input and output v
Wiener filter
In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process, assuming kn
Kautz filter
In signal processing, the Kautz filter, named after William H. Kautz, is a fixed-pole traversal filter, published in 1954. Like , Kautz filters can be implemented using a cascade of all-pass filters,
Capacitor-input filter
A capacitor-input filter is a filter circuit in which the first element is a capacitor connected in parallel with the output of the rectifier in a linear power supply. The capacitor increases the DC v
Antimetric electrical network
An antimetric electrical network is an electrical network that exhibits anti-symmetrical electrical properties. The term is often encountered in filter theory, but it applies to general electrical net
Gammatone filter
A gammatone filter is a linear filter described by an impulse response that is the product of a gamma distribution and sinusoidal tone. It is a widely used model of auditory filters in the auditory sy
Root-raised-cosine filter
In signal processing, a root-raised-cosine filter (RRC), sometimes known as square-root-raised-cosine filter (SRRC), is frequently used as the transmit and receive filter in a digital communication sy
Unscented transform
The unscented transform (UT) is a mathematical function used to estimate the result of applying a given nonlinear transformation to a probability distribution that is characterized only in terms of a
Switching Kalman filter
The switching Kalman filtering (SKF) method is a variant of the Kalman filter. In its generalised form, it is often attributed to Kevin P. Murphy, but related switching state-space models have been in
Bessel filter
In electronics and signal processing, a Bessel filter is a type of analog linear filter with a maximally flat group/phase delay (maximally linear phase response), which preserves the wave shape of fil
Waveguide filter
A waveguide filter is an electronic filter constructed with waveguide technology. Waveguides are hollow metal conduits inside which an electromagnetic wave may be transmitted. Filters are devices used
Kalman filter
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise