This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Nonlinear filter" – news · newspapers · books · scholar · JSTOR(October 2018) (Learn how and when to remove this message)
In signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals R and S for two input signals r and s separately, but does not always output αR + βS when the input is a linear combination αr + βs.
Both continuous-domain and discrete-domain filters may be nonlinear. A simple example of the former would be an electrical device whose output voltage R(t) at any moment is the square of the input voltage r(t); or which is the input clipped to a fixed range [a,b], namely R(t) = max(a, min(b, r(t))). An important example of the latter is the running-median filter, such that every output sample Ri is the median of the last three input samples ri, ri−1, ri−2. Like linear filters, nonlinear filters may be shift invariant or not.
Non-linear filters have many applications, especially in the removal of certain types of noise that are not additive. For example, the median filter is widely used to remove spike noise — that affects only a small percentage of the samples, possibly by very large amounts. Indeed, all radio receivers use non-linear filters to convert kilo- to gigahertz signals to the audio frequency range; and all digital signal processing depends on non-linear filters (analog-to-digital converters) to transform analog signals to binary numbers.
However, nonlinear filters are considerably harder to use and design than linear ones, because the most powerful mathematical tools of signal analysis (such as the impulse response and the frequency response) cannot be used on them. Thus, for example, linear filters are often used to remove noise and distortion that was created by nonlinear processes, simply because the proper non-linear filter would be too hard to design and construct.
From the foregoing, we can know that the nonlinear filters have quite different behavior compared to linear filters. The most important characteristic is that, for nonlinear filters, the filter output or response of the filter does not obey the principles outlined earlier, particularly scaling and shift invariance. Furthermore, a nonlinear filter can produce results that vary in a non-intuitive manner.
processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals...
sometimes termed the Stratonovich–Kalman–Bucy filter because it is a special case of a more general, nonlinearfilter developed somewhat earlier by the Soviet...
filtering problems for nonlinear state-space systems, such as signal processing and Bayesian statistical inference. The filtering problem consists of estimating...
In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current...
Methods for Nonlinear System Modeling. Elsevier Inc. ISBN 978-0-12-812976-0. M.Poluektov and A.Polar. Urysohn Adaptive Filter. 2019. "Nonlinear Adaptive...
The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential...
machine learning, recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability...
(2005). Nonlinear Signal Processing: A Statistical Approach. New Jersey, USA: Wiley. ISBN 0-471-67624-1. Fast MATLAB one-dimensional median filter implementation...
support for legal proceedings. Brigo holds a Ph.D. in stochastic nonlinearfiltering with differential geometric methods from the Free University of Amsterdam...
context of signal processing, an unsharp mask is generally a linear or nonlinearfilter that amplifies the high-frequency components of a signal. For the photographic...
transform is in the nonlinear projection of mean and covariance estimates in the context of nonlinear extensions of the Kalman filter. Its creator Jeffrey...
Generalized filtering is a generic Bayesian filtering scheme for nonlinear state-space models. It is based on a variational principle of least action,...
nonlinear systems possessing symmetries (or invariances), then generalized and recast as an adaptation to Lie groups of the linear Kalman filtering theory...
two-sample Student's t-test. Alternatively, a nonlinearfilter such as the median filter is applied to the signal. Filters such as these attempt to remove the noise...
that relies on linear programming or nonlinear programming solvers to find a solution. MHE reduces to the Kalman filter under certain simplifying conditions...
used to find approximate solutions for filtering problems for nonlinear state-space systems. The filtering problem consists of estimating the unobserved...
frequency Filter design Laplace transform Green's function Prototype filter Z-transform System theory LTI system theory Nonlinearfilter Wiener filter Gabor...
Homomorphic filtering is a generalized technique for signal and image processing, involving a nonlinear mapping to a different domain in which linear filter techniques...
Kalman filters. More recent implementations of soft sensors use neural networks or fuzzy computing. Examples of soft sensor applications: Kalman filters for...
as total variation regularization or total variation filtering, is a noise removal process (filter). It is based on the principle that signals with excessive...
signal processing, a kernel adaptive filter is a type of nonlinear adaptive filter. An adaptive filter is a filter that adapts its transfer function to...
blurring, linear filters are seldom used in practice for noise reduction;[citation needed] they are, however, often used as the basis for nonlinear noise reduction...
The auxiliary particle filter is a particle filtering algorithm introduced by Pitt and Shephard in 1999 to improve some deficiencies of the sequential...
distributions of the current random states (see McKean–Vlasov processes, nonlinearfiltering equation). In other instances we are given a flow of probability...
than their topology. Transfer functions may be linear or nonlinear. Common types of linear filter transfer function are; high-pass, low-pass, bandpass, band-reject...
Global Information