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65 relations: Additive white Gaussian noise, Autocorrelation, Bayesian inference, Cambridge University Press, Cauchy–Schwarz inequality, Channel capacity, Complex conjugate, Conjugate transpose, Convolution, Covariance matrix, Cross-correlation, Data transmission, Detection theory, Digital filter, Digital image processing, Discrete Fourier transform, Discrete time and continuous time, Doppler effect, Edwin Thompson Jaynes, Estimation theory, Expected value, First observation of gravitational waves, Gaussian noise, Gravitational-wave astronomy, Hermitian matrix, Heteroscedasticity, Impulse response, Inner product space, Lagrange multiplier, Least mean squares filter, Least squares, Likelihood function, Linear filter, Linear time-invariant theory, Maximum likelihood estimation, Moving target indication, Multiple comparisons problem, MUSIC (algorithm), Neyman–Pearson lemma, Noise (signal processing), Noisy-channel coding theorem, Non-return-to-zero, Pergamon Press, Periodogram, Philip Woodward, Prentice Hall, Pulse compression, Radar, Rectangular function, Resampling (statistics), ..., SAMV (algorithm), Signal, Signal processing, Signal-to-noise ratio, Spectral density, Spectral density estimation, Statistical signal processing, Statistical significance, Stochastic process, Super-resolution imaging, Type I and type II errors, White noise, Whitening transformation, Whittle likelihood, Wiener filter. Expand index (15 more) »
Additive white Gaussian noise
Additive white Gaussian noise (AWGN) is a basic noise model used in Information theory to mimic the effect of many random processes that occur in nature.
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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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Bayesian inference
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Cauchy–Schwarz inequality
In mathematics, the Cauchy–Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas.
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Channel capacity
Channel capacity, in electrical engineering, computer science and information theory, is the tight upper bound on the rate at which information can be reliably transmitted over a communication channel.
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Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
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Conjugate transpose
In mathematics, the conjugate transpose or Hermitian transpose of an m-by-n matrix A with complex entries is the n-by-m matrix A∗ obtained from A by taking the transpose and then taking the complex conjugate of each entry.
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Convolution
In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.
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Covariance matrix
In probability theory and statistics, a covariance matrix (also known as dispersion matrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i-th and j-th elements of a random vector.
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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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Data transmission
Data transmission (also data communication or digital communications) is the transfer of data (a digital bitstream or a digitized analog signal) over a point-to-point or point-to-multipoint communication channel.
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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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Digital filter
In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal.
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Digital image processing
In computer science, Digital image processing is the use of computer algorithms to perform image processing on digital images.
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Discrete Fourier transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
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Discrete time and continuous time
In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.
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Doppler effect
The Doppler effect (or the Doppler shift) is the change in frequency or wavelength of a wave in relation to observer who is moving relative to the wave source.
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Edwin Thompson Jaynes
Edwin Thompson Jaynes (July 5, 1922 – April 30, 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis.
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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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Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
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First observation of gravitational waves
The first observation of gravitational waves was made on 14 September 2015 and was announced by the LIGO and Virgo collaborations on 11 February 2016.
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Gaussian noise
Gaussian noise is statistical noise having a probability density function (PDF) equal to that of the normal distribution, which is also known as the Gaussian distribution.
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Gravitational-wave astronomy
Gravitational-wave astronomy is an emerging branch of observational astronomy which aims to use gravitational waves (minute distortions of spacetime predicted by Einstein's theory of general relativity) to collect observational data about objects such as neutron stars and black holes, events such as supernovae, and processes including those of the early universe shortly after the Big Bang.
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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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Heteroscedasticity
In statistics, a collection of random variables is heteroscedastic (or heteroskedastic; from Ancient Greek hetero “different” and skedasis “dispersion”) if there are sub-populations that have different variabilities from others.
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Impulse response
In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse.
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Lagrange multiplier
In mathematical optimization, the method of Lagrange multipliers (named after Joseph-Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).
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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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Likelihood function
In frequentist inference, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, given specific observed data.
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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 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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Maximum likelihood estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.
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Moving target indication
Moving target indication (MTI) is a mode of operation of a radar to discriminate a target against the clutter.
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Multiple comparisons problem
In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or infers a subset of parameters selected based on the observed values.
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MUSIC (algorithm)
MUSIC (MUltiple SIgnal Classification) is an algorithm used for frequency estimation and emitter location.
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Neyman–Pearson lemma
In statistics, the Neyman–Pearson lemma was introduced by Jerzy Neyman and Egon Pearson in a paper in 1933.
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Noise (signal processing)
In signal processing, noise is a general term for unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion.
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Noisy-channel coding theorem
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.
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Non-return-to-zero
In telecommunication, a non-return-to-zero (NRZ) line code is a binary code in which ones are represented by one significant condition, usually a positive voltage, while zeros are represented by some other significant condition, usually a negative voltage, with no other neutral or rest condition.
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Pergamon Press
Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, which published scientific and medical books and journals.
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Periodogram
In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898.
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Philip Woodward
Philip Mayne Woodward (6 September 1919 – 30 January 2018) was a British mathematician, radar engineer and horologist.
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Prentice Hall
Prentice Hall is a major educational publisher owned by Pearson plc.
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Pulse compression
Pulse compression is a signal processing technique commonly used by radar, sonar and echography to increase the range resolution as well as the signal to noise ratio.
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Radar
Radar is an object-detection system that uses radio waves to determine the range, angle, or velocity of objects.
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Rectangular function
The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as: 0 & \mbox |t| > \frac \\ \frac & \mbox |t|.
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Resampling (statistics)
In statistics, resampling is any of a variety of methods for doing one of the following.
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SAMV (algorithm)
SAMV (iterative Sparse Asymptotic Minimum Variance) is a parameter-free superresolution algorithm for spectral estimation and direction-of-arrival (DOA) estimation in signal processing.
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Signal
A signal as referred to in communication systems, signal processing, and electrical engineering is a function that "conveys information about the behavior or attributes of some phenomenon".
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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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Signal-to-noise ratio
Signal-to-noise ratio (abbreviated SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise.
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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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Spectral density estimation
In statistical signal processing, the goal of spectral density estimation (SDE) is to estimate the spectral density (also known as the power spectral density) of a random signal from a sequence of time samples of the signal.
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Statistical signal processing
Statistical signal processing is an approach to signal processing which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks.
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Statistical significance
In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis.
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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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Super-resolution imaging
Super-resolution imaging (SR) is a class of techniques that enhance the resolution of an imaging system.
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Type I and type II errors
In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is failing to reject a false null hypothesis (also known as a "false negative" finding).
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White noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.
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Whitening transformation
A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they are uncorrelated and each have variance 1.
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Whittle likelihood
In statistics, Whittle likelihood is an approximation to the likelihood function of a stationary Gaussian time series.
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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 known stationary signal and noise spectra, and additive noise.
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References
[1] https://en.wikipedia.org/wiki/Matched_filter
