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The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance. Specifically, it calculates
Autocorrelation_technique
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself.
Autocorrelation
Autocorrelation functions realized in optics
following examples, the autocorrelation signal is generated by the nonlinear process of second-harmonic generation (SHG). Other techniques based on two-photon
Optical_autocorrelation
Techniques to study geometric data
to the spatial autocorrelation problem in statistics since, like temporal autocorrelation, this violates standard statistical techniques that assume independence
Spatial_analysis
American geographer and spatial statistician
spatial filtering (MESF) technique and introducing the sui-random variables model, both of which address spatial autocorrelation in regression modeling
Daniel_A._Griffith
Lag windowing is a technique that consists of windowing the autocorrelation coefficients prior to estimating linear prediction coefficients (LPC). The
Lag_windowing
Optical device for selecting part of a spectrum
measurement is performed in the time domain, using the field autocorrelation technique. Polychromator Ultrafast monochromator – a monochromator that
Monochromator
Sequence of digital values used for synchronisation
Barker sequence is a finite sequence of digital values with the ideal autocorrelation property. It is used as a synchronising pattern between the sender
Barker_code
Method to find best fit of a time-series model
differencing it if necessary), and using plots of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the dependent time series to decide
Box–Jenkins_method
Chart of correlation statistics
statistics. For example, in time series analysis, a plot of the sample autocorrelations r h {\displaystyle r_{h}} versus h {\displaystyle h\,} (the time lags)
Correlogram
Type of radar system
radar presentation, which highlights the advantages of using the autocorrelation technique Pulse-Doppler radar handouts from Introduction to Principles and
Pulse-Doppler_radar
Technique for determining size distribution of particles
temporal fluctuations are usually analyzed using the intensity or photon autocorrelation function (also known as photon correlation spectroscopy – PCS or quasi-elastic
Dynamic_light_scattering
interferometric autocorrelator is an electronic tool used to examine the autocorrelation of, among other things, optical beam intensity and spectral components
Autocorrelator
Calculation of complex statistical distributions
the proposal to adapt over time. Parameter blocking is a technique that reduces autocorrelation in MCMC by updating parameters jointly rather than one at
Markov_chain_Monte_Carlo
Measure of spatial autocorrelation
Moran's I is a measure of spatial autocorrelation developed by Patrick Alfred Pierce Moran. Spatial autocorrelation is characterized by a correlation
Moran's_I
Medical diagnostic method
analysis (spectral density estimation) as pulsed Doppler and by the autocorrelation technique as colour tissue Doppler (duplex ultrasonography). While pulsed
Tissue Doppler echocardiography
Tissue_Doppler_echocardiography
Mathematical technique in spectroscopic analysis
also called autopeaks and the main diagonal signal is referred to as autocorrelation signal. The off-diagonal cross-peaks can be either positive or negative
Two-dimensional correlation analysis
Two-dimensional_correlation_analysis
Power spectrum of a noise signal
analysis and market forecasting. There are two algorithms based on autocorrelation functions that can identify the dominant noise type in a data set provided
Colors_of_noise
Type of statistical analysis
chemical reactions, aggregation, etc.) are analyzed using the temporal autocorrelation. Because the measured property is essentially related to the magnitude
Fluorescence correlation spectroscopy
Fluorescence_correlation_spectroscopy
Probabilistic problem-solving algorithm
traditional Monte Carlo and MCMC methodologies, these mean-field particle techniques rely on sequential interacting samples. The terminology mean field reflects
Monte_Carlo_method
Representation of a type of random process
The autocorrelation function of an AR(p) process is a sum of decaying exponentials. Each real root contributes a component to the autocorrelation function
Autoregressive_model
Source of statistical bias
However, the daily data in the example may have too much noise, temporal autocorrelation, or be inconsistent with other datasets. With only daily data, conducting
Modifiable temporal unit problem
Modifiable_temporal_unit_problem
Medical imaging and optical technique
electric field temporal autocorrelation function is measured. A model for photon propagation through tissues, the measured autocorrelation signal is used to
Diffuse correlation spectrometry
Diffuse_correlation_spectrometry
Method for visualizing and analyzing particles in liquids
exponential autocorrelation function, average particle size can be calculated as well as a polydispersity index. For multi-exponential autocorrelation functions
Nanoparticle tracking analysis
Nanoparticle_tracking_analysis
Method of measuring spectral phase of ultrashort laser pulses
is currently the standard technique for measuring ultrashort laser pulses replacing an older method called autocorrelation, which only gave a rough estimate
Frequency-resolved optical gating
Frequency-resolved_optical_gating
Measure of the long-range dependence of a time series
as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag
Hurst_exponent
Process of reducing correlation within one or more signals
Decorrelation is a general term for any process that is used to reduce autocorrelation within a signal, or cross-correlation within a set of signals, while
Decorrelation
Study of spatial information
in data that underlie many techniques and technologies employed and investigated by technical geographers. Autocorrelation is a statistical measure used
Technical_geography
Type of stochastic process
identifying non-stationary time series is the ACF (Autocorrelation Function) plot, which plots the autocorrelation against the lag. Sometimes, patterns related
Stationary_process
Correlation as a function of distance
points, then this is often referred to as an autocorrelation function, which is made up of autocorrelations. Correlation functions of different random variables
Correlation_function
Method to detect power-law scaling in time series
with time). It is related to measures based upon spectral techniques such as autocorrelation and Fourier transform. Peng et al. introduced DFA in 1994
Detrended fluctuation analysis
Detrended_fluctuation_analysis
Spectral density estimation method
corresponds to the most random or the most unpredictable time series whose autocorrelation function agrees with the known values. This assumption, which corresponds
Maximum entropy spectral estimation
Maximum_entropy_spectral_estimation
Statistical measure
standard errors are consistent in the presence of accurately-modeled autocorrelation, clustered standard errors are consistent in the presence of cluster-based
Clustered_standard_errors
increases then overlap save sectioning technique would be applied.[clarification needed] If the autocorrelation function in Blackman–Tukey is computed
Blackman–Tukey_transformation
Images used to represent statistical data visually
Statistical graphics, also known as statistical graphical techniques, are graphics used in the field of statistics for data visualization. Whereas statistics
Statistical_graphics
Algorithm used for frequency estimation and radio direction finding
the p × p {\displaystyle p\times p} autocorrelation matrix of s {\displaystyle \mathbf {s} } . The autocorrelation matrix R x {\displaystyle \mathbf {R}
MUSIC_(algorithm)
Statistical model validation technique
challenges occur with spatial and spatiotemporal data, where spatial autocorrelation can lead to overly optimistic error estimates when random splits are
Cross-validation_(statistics)
scale. The basic concepts involved in spectral estimation include autocorrelation, multi-D Fourier transform, mean square error and entropy. When it
Multidimensional spectral estimation
Multidimensional_spectral_estimation
Type of statistics
collection of summarisation techniques has been formulated under the heading of exploratory data analysis: an example of such a technique is the box plot. In
Descriptive_statistics
Relative importance of certain frequencies in a composite signal
function S ¯ x x ( f ) {\displaystyle {\bar {S}}_{xx}(f)} and the autocorrelation of x ( t ) {\displaystyle x(t)} form a Fourier transform pair, a result
Spectral_density
Signal with properties that vary cyclically with time
that exhibits cyclostationarity in second-order statistics (e.g., the autocorrelation function). These are called wide-sense cyclostationary signals, and
Cyclostationary_process
Statistical model used in time series analysis
determined using the sample autocorrelation function (ACF), partial autocorrelation function (PACF), and/or extended autocorrelation function (EACF) method
Autoregressive integrated moving average
Autoregressive_integrated_moving_average
Selection of data points in statistics
instance) selected at the last step of this procedure are then surveyed. This technique, thus, is essentially the process of taking random subsamples of preceding
Sampling_(statistics)
Multivariate statistical technique
identify non-trivial spatial genetic patterns. By accounting for spatial autocorrelation, sPCA is able to uncover spatial patterns in the data and find the
Spatial Analysis of Principal Components
Spatial_Analysis_of_Principal_Components
Algorithm to estimate signal frequency
ASMDF (Average Squared Mean Difference Function), and other similar autocorrelation algorithms work this way. These algorithms can give quite accurate
Pitch_detection_algorithm
Audio processor that alters pitch
Macintosh computer. Hildebrand's method for detecting pitch involved autocorrelation and proved superior to attempts based on feature extraction, which
AutoTune
Function returning one of only two values
ones in the truth table. Bent: its derivatives are all balanced (the autocorrelation spectrum is zero) Correlation immune to mth order: if the output is
Boolean_function
8-Meter Solar Telescope. JDSO 11(1s): 302. Wiley, E. O. 2015. Autocorrelation techniques with small telescopes with comments on lucky imaging. In: Double
Edward_O._Wiley
Spectroscopy based on time- or space-domain data
methods for measuring the temporal coherence of the light (see: field-autocorrelation), including the continuous-wave and the pulsed Fourier-transform spectrometer
Fourier-transform spectroscopy
Fourier-transform_spectroscopy
Graph showing the rate of water flow
up in the basin during the earlier phases of the hydrograph. Lag-1 autocorrelation method to compare streamflow data to itself by shifting or "lagging"
Hydrograph
Changing the speed or duration of an audio signal without affecting its pitch
some pitch detection algorithm (commonly the peak of the signal's autocorrelation, or sometimes cepstral processing), and crossfade one period into another
Audio time stretching and pitch scaling
Audio_time_stretching_and_pitch_scaling
based on the use of various statistical methods (such as phylogenetic autocorrelation coefficients, phylogenetic correlograms, as well as autoregressive
Phylogenetic_signal
Type of pseudorandom binary sequence
One eighth of the runs are of length 3. ... etc. ... The circular autocorrelation of an MLS is a Kronecker delta function (with DC offset and time delay
Maximum-length_sequence
Free geovisualization and analysis software
package that conducts spatial data analysis, geovisualization, spatial autocorrelation and spatial modeling. It runs on different versions of Windows, Mac
GeoDa
Series of geography texts, 1975–1996
(2): 181–188. Cox, Nicholas J. (1989). "Teaching and learning spatial autocorrelation: a review". Journal of Geography in Higher Education. 13 (2): 185–190
Concepts and Techniques in Modern Geography
Concepts_and_Techniques_in_Modern_Geography
back through the same channel, effectively autocorrelating it. This autocorrelation function has a peak at the origin, where the original source was. The
Time reversal signal processing
Time_reversal_signal_processing
graph Entity-relationship diagram Tag cloud, also known as word cloud Autocorrelation plot Bar chart Biplot Box plot Bullet graph Chernoff faces Control
List_of_graphical_methods
Statistical proof by contradiction technique
structure of the original series (for instance, by preserving the autocorrelation function, or equivalently the periodogram, an estimate of the sample
Surrogate_data_testing
Measure of covariance of components of a random vector
{\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }} is related to the autocorrelation matrix R X X {\displaystyle \operatorname {R} _{\mathbf {X} \mathbf
Covariance_matrix
Thematic map visualizing multiple variables
maps. The technique works best when the variables happen to have a clear geographic pattern, such as a high degree of spatial autocorrelation, so that
Multivariate_map
Laser pulse with duration a picosecond (10^-12 s) or less
gating (FROG) is a nonlinear technique that yields the intensity and phase of a pulse. It is a spectrally resolved autocorrelation. The algorithm that extracts
Ultrashort_pulse
Koteswara Rao (1968). "A Transformation Used to Circumvent the Problem of Autocorrelation". Econometrica. 36 (1): 93–96. doi:10.2307/1909605. JSTOR 1909605.
Cochrane–Orcutt_estimation
1969 law by Waldo Tobler
foundation of the fundamental concepts of spatial dependence and spatial autocorrelation and is utilized specifically for the inverse distance weighting method
Tobler's first law of geography
Tobler's_first_law_of_geography
Seemingly random, difficult to predict bit stream created by a deterministic algorithm
{\displaystyle N-m} zeros. A BS is a pseudorandom binary sequence (PRBS) if its autocorrelation function, given by C ( v ) = ∑ j = 0 N − 1 a j a j + v {\displaystyle
Pseudorandom_binary_sequence
Optical technique for monitoring brain activity
quantified by the temporal intensity autocorrelation curve of a single speckle. The decay of the autocorrelation curve is fitted with the solution of
Functional near-infrared spectroscopy
Functional_near-infrared_spectroscopy
Phenomenon in economics and accounting
positive autocorrelations for the first three lags that decline in magnitude: First-order autocorrelation: approximately 0.34 Second-order autocorrelation: approximately
Post–earnings-announcement drift
Post–earnings-announcement_drift
Signal processing algorithm
stochastic processes with known spectral characteristics or known autocorrelation and cross-correlation Requirement: the filter must be physically realizable/causal
Wiener_filter
difference increases. The sum of the autocorrelation function over all lags is finite. As the lag increases, the autocorrelation function of short-range dependent
Long-tail_traffic
Audio compression standard
envelope. The pitch period is estimated from the peak values of the autocorrelation of the residual signal. In this process, the residual signal is compared
Harmonic Vector Excitation Coding
Harmonic_Vector_Excitation_Coding
correlation is the bispectrum. The triple correlation extends the concept of autocorrelation, which correlates a function with a single shifted copy of itself and
Triple_correlation
Statistical model used in time series analysis
be found by plotting the partial autocorrelation functions. Similarly, q can be estimated by using the autocorrelation functions. Both p and q can be determined
Autoregressive moving-average model
Autoregressive_moving-average_model
One of several proposed laws of geography
of geography and Tobler's second law of geography emphaize spatial autocorrelation and the boundary problem, Arbia's law of geography deals with Spatial
Arbia's_law_of_geography
Imaging and diffraction using electrons that pass through samples
Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The
Transmission electron microscopy
Transmission_electron_microscopy
Spectroscopic technique
spectroscopy (/ˈrɑːmən/; named after physicist C. V. Raman) is a spectroscopic technique typically used to determine vibrational modes of molecules, although rotational
Raman_spectroscopy
of the speckle pattern will be used to compute the contrast value. Autocorrelation functions of electric field are used to measure the relationship between
Laser speckle contrast imaging
Laser_speckle_contrast_imaging
Variations in data at specific regular intervals less than a year
if the period is not known, the autocorrelation plot can help. If there is significant seasonality, the autocorrelation plot should show spikes at lags
Seasonality
Estimation procedure for correlated data
efficiency than generalized linear models (GLMs) in the presence of high autocorrelation. When the true working correlation is known, consistency does not require
Generalized estimating equation
Generalized_estimating_equation
Statistical sampling technique
Michael McKay of Los Alamos National Laboratory in 1979. An equivalent technique was independently proposed by Vilnis Eglājs in 1977. It was further elaborated
Latin_hypercube_sampling
American physicist (1925–2020)
the liquid-solid phase transition for hard sphere and the velocity autocorrelations function decay in liquids. Alder, along with Teller, was one of the
Berni_Alder
which the scattering light is mixed with the reference light. The autocorrelation function of intensity of the mixed light, g ( τ ) {\displaystyle g(\tau
Electrophoretic light scattering
Electrophoretic_light_scattering
Theorem related to ordinary least squares
declines over time. This assumption is violated when there is autocorrelation. Autocorrelation can be visualized on a data plot when a given observation is
Gauss–Markov_theorem
Wireless networking standard
for OFDM but was also suitable for use in 802.11b because of its low autocorrelation properties. The dramatic increase in throughput of 802.11b (compared
IEEE_802.11b-1999
diffusing-wave spectroscopy The signal is analysed by calculating the intensity autocorrelation function called g2. g 2 ( τ ) = ⟨ I ( t ) I ( t + τ ) ⟩ t ⟨ I ( t )
Diffusing-wave_spectroscopy
Signal processing technique
Pulse compression is a signal processing technique commonly used by radar, sonar and echography to either increase the range resolution when pulse length
Pulse_compression
Area of research in signal processing
S_{\text{XX}}(f)} of a signal is related to its autocorrelation function by a Fourier transform: where the autocorrelation function R XX ( τ ) {\displaystyle R_{\text{XX}}(\tau
Array_processing
Overview of and topical guide to regression analysis
Coefficient of determination Multiple correlation Scheffé's method Autocorrelation Cointegration Multicollinearity Homoscedasticity and heteroscedasticity
Outline of regression analysis
Outline_of_regression_analysis
Way to produce very short laser bursts
directly measured using optoelectronic techniques (i.e. photodiodes), and so indirect methods, such as autocorrelation, frequency-resolved optical gating
Mode_locking
Sequence of data points over time
filter; see filtering and smoothing for more techniques. Other related techniques include: Autocorrelation analysis to examine serial dependence Spectral
Time_series
British physicist (1915–2015)
first described by Barker in 1953. These sequences have favourable autocorrelation properties that allow reliable detection and timing synchronisation
Ronald_Hugh_Barker
Seismologist at Stanford University
2 hours, 140 times faster than the traditional autocorrelation method. Furthermore, the new technique would help better monitor and categorize earthquakes
Gregory_Beroza
Method of statistical inference
conviction, the defendant is guilty." Statistical hypothesis testing is a key technique of both frequentist inference and Bayesian inference, although the two
Statistical_hypothesis_test
Method of measuring ultrashort laser pulses
developed based on quasi instantaneous non linear optical effects such as autocorrelation, FROG, SPIDER, etc. However, these can only measure the pulse characteristics
Multiphoton intrapulse interference phase scan
Multiphoton_intrapulse_interference_phase_scan
Statistical method
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study
Matching_(statistics)
Hybrid type of thematic map
modeled by the original choropleth map has a high degree of spatial autocorrelation; that is, the real-world spatial transitions in population density
Dasymetric_map
Basic component of symmetric key algorithms
(LAT) or Walsh transform and Difference Distribution Table (DDT) or autocorrelation table and spectrum. Its strength may be summarized by the nonlinearity
S-box
Study of survey methods
studies the sampling of individual units from a population and associated techniques of survey data collection, such as questionnaire construction and methods
Survey_methodology
Nonlinear optical process
measurements. Optical autocorrelation, in its intensity or fringe-resolved (interferometric) versions, uses SHG, unlike linear field autocorrelation. Also, most
Second-harmonic_generation
Method of data analysis
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data
Principal_component_analysis
Diagram showing crime incident patterns
data analysis techniques that add statistical rigor and address inherent limitations of spatial data, including spatial autocorrelation and spatial heterogeneity
Crime_mapping
Method to measure velocities in fluid
for each window with help of signal processing and autocorrelation or cross-correlation techniques. This is converted to a velocity using the time between
Particle_image_velocimetry
AUTOCORRELATION TECHNIQUE
AUTOCORRELATION TECHNIQUE
AUTOCORRELATION TECHNIQUE
AUTOCORRELATION TECHNIQUE
AUTOCORRELATION TECHNIQUE
AUTOCORRELATION TECHNIQUE
AUTOCORRELATION TECHNIQUE
AUTOCORRELATION TECHNIQUE
AUTOCORRELATION TECHNIQUE