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45 relations: Ali H. Sayed, Andrey Kolmogorov, Autocorrelation, Babak Hassibi, Causal system, Cross-correlation, Deconvolution, Detection theory, Eberhard Hopf, Estimation theory, Filter (signal processing), Finite impulse response, Frequency response, Generalized Wiener filter, Hermitian matrix, Information field theory, Kalman filter, Kriging, Laplace transform, Least mean squares filter, Least squares, Levinson recursion, Linear filter, Linear prediction, Linear time-invariant theory, Matched filter, Minimum mean square error, Noise, Noise reduction, Norbert Wiener, Norman Levinson, Partial fraction decomposition, Signal processing, Similarities between Wiener and LMS, Spectral density, Speech recognition, Stationary process, Statistics, Stochastic process, Symmetric matrix, System identification, Thomas Kailath, Toeplitz matrix, Wiener deconvolution, Wiener–Hopf method.
Ali H. Sayed
Ali H. Sayed (born Sao Paulo, Brazil, to parents of Lebanese descent) is Professor of Electrical Engineering at the University of California, Los Angeles (UCLA), where he teaches and conducts research on Adaptation, Learning, Statistical Signal Processing, and Signal Processing for Communications.
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Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a 20th-century Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.
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Autocorrelation
Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay.
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Babak Hassibi
Babak Hassibi (بابک حسیبی, born in Tehran, Iran) is an Iranian-American electrical engineer who is the inaugural Mose and Lillian S. Bohn Professor of Electrical Engineering at the California Institute of Technology (Caltech).
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Causal system
In control theory, a causal system (also known as a physical or nonanticipative system) is a system where the output depends on past and current inputs but not future inputs—i.e., the output y(t_) depends on only the input x(t) for values of t \le t_.
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Cross-correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other.
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Deconvolution
In mathematics, deconvolution is an algorithm-based process used to reverse the effects of convolution on recorded data.
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Detection theory
Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the detection machine and of the nervous system of the operator).
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Eberhard Hopf
Eberhard Frederich Ferdinand Hopf (April 17, 1902, Salzburg, Austria-Hungary – July 24, 1983, Bloomington, Indiana) was a mathematician and astronomer, one of the founding fathers of ergodic theory and a pioneer of bifurcation theory who also made significant contributions to the subjects of partial differential equations and integral equations, fluid dynamics, and differential geometry.
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Estimation theory
Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component.
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Filter (signal processing)
In signal processing, a filter is a device or process that removes some unwanted components or features from a signal.
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Finite impulse response
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time.
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Frequency response
Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system.
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Generalized Wiener filter
The Wiener filter as originally proposed by Norbert Wiener is a signal processing filter which uses knowledge of the statistical properties of both the signal and the noise to reconstruct an optimal estimate of the signal from a noisy one-dimensional time-ordered data stream.
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Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
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Information field theory
Information field theory (IFT) is a Bayesian statistical field theory relating to signal reconstruction, cosmography, and other related areas.
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Kalman filter
Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe.
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Kriging
In statistics, originally in geostatistics, kriging or Gaussian process regression is a method of interpolation for which the interpolated values are modeled by a Gaussian process governed by prior covariances, as opposed to a piecewise-polynomial spline chosen to optimize smoothness of the fitted values.
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Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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Least mean squares filter
Least mean squares (LMS) algorithms are a class of adaptive filter used to mimic a desired filter by finding the filter coefficients that relate to producing the least mean square of the error signal (difference between the desired and the actual signal).
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Least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
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Levinson recursion
Levinson recursion or Levinson–Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix.
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Linear filter
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity.
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Linear prediction
Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples.
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Linear time-invariant theory
Linear time-invariant theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas.
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Matched filter
In signal processing, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.
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Minimum mean square error
In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable.
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Noise
Noise is unwanted sound judged to be unpleasant, loud or disruptive to hearing.
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Noise reduction
Noise reduction is the process of removing noise from a signal.
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Norbert Wiener
Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher.
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Norman Levinson
Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician.
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Partial fraction decomposition
In algebra, the partial fraction decomposition or partial fraction expansion of a rational function (that is, a fraction such that the numerator and the denominator are both polynomials) is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
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Signal processing
Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.
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Similarities between Wiener and LMS
The Least mean squares filter solution converges to the Wiener filter solution, assuming that the unknown system is LTI and the noise is stationary.
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Spectral density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal.
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Speech recognition
Speech recognition is the inter-disciplinary sub-field of computational linguistics that develops methodologies and technologies that enables the recognition and translation of spoken language into text by computers.
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Stationary process
In mathematics and statistics, a stationary process (a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.
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Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
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Stochastic process
--> In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.
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Symmetric matrix
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.
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System identification
The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data.
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Thomas Kailath
Thomas Kailath (born June 7, 1935) is an electrical engineer, information theorist, control engineer, entrepreneur and the Hitachi America Professor of Engineering, Emeritus, at Stanford University.
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Toeplitz matrix
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant.
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Wiener deconvolution
In mathematics, Wiener deconvolution is an application of the Wiener filter to the noise problems inherent in deconvolution.
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Wiener–Hopf method
The Wiener–Hopf method is a mathematical technique widely used in applied mathematics.
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Kolmogorov-Wiener filter, Weiner filter, Wiener filtering, Wienerov filter.
References
[1] https://en.wikipedia.org/wiki/Wiener_filter
