Autocorrelation is the cross-correlation of a signal with itself.

* Autocorrelation is used to analyze Dynamic light scattering data, which notably enables to determine the particle size distributions of nanometer-sized particles or micelles suspended in a fluid.

* Autocorrelation in space rather than time, via the Patterson function, is used by X-ray diffractionists to help recover the " Fourier phase information " on atom positions not available through diffraction alone.

Autocorrelation can be visualized on a data plot when a given observation is more likely to lie above a fitted line if adjacent observations also lie above the fitted regression line.

Autocorrelation is common in time series data where a data series may experience " inertia.

Autocorrelation of the signal can be analyzed in terms of the diffusion of the particles.

* Autocorrelation detects signal waveforms.

* Autocorrelation function, mathematical tool used frequently in signal processing

Autocorrelation of the errors, which themselves are unobserved, can generally be detected because it produces autocorrelation in the observable residuals.

Autocorrelation violates the ordinary least squares ( OLS ) assumption that the error terms are uncorrelated.

* Autocorrelation articles in Comp. DSP ( DSP usenet group ).

Autocorrelation may be the result of misspecification such as choosing the wrong functional form.

Autocorrelation methods need at least two pitch periods to detect pitch.

* Sieves for Low Autocorrelation Binary Sequences, IEEE Trans.

Autocorrelation analysis helps to identify the correct phase of the fitted model while the successive differencing transforms the stochastic drift component into white noise.

A new South is emerging after the post-bellum years of hesitation, uncertainty, and lack of action from the Negro in defining his new role in the amorphously defined socio-political organizations of the white man.

A small business is defined as one which is independently owned and operated and which is not dominant in its field.

Field shifts were derived from the mean value of the resonance line, defined as the field about which the first moment is zero.

Dirt, which is here defined as particulate material which is usually inorganic and is very often extremely finely divided so as to exhibit colloidal properties.

The international unit is equipotent with the USP unit adopted in 1952, which was defined as the amount of activity present in 20 mg of the USP reference substance.

The function f{t} defined in this way is multi-valued.

In some neighborhood of an isolated tangent point in the f-plane, say Af, the function Af is either double-valued or has no values defined, except at the tangent point itself, where it is single-valued.

Suppose Af is defined in the sub-interval Af.

Where boundary maintenance describes the boundaries or limits of the group, systemic linkage is defined `` as the process whereby one or more of the elements of at least two social systems is articulated in such a manner that the two systems in some ways and on some occasions may be viewed as a single unit.

The positive Kohnstamm reactivity in Condition 1 ( ( the naive state ) is not adequately explained by such a concept as suggestibility ( if suggestibility is defined as the influence on behavior by verbal cues ).

For example, property `` used in the trade or business '' of a transferor corporation, as defined in section 1231, presumably would not retain its special status following a non-taxable reorganization if it is not so used in the business of the acquiring corporation.

Planes defined as parallel to the surface also cut through it into real space, and a depth is suggested optically which is greater than that established pictorially.

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The gyro angular momentum is defined by H.

But since this is a world in which people disagree about ends and goals and concerning justice and injustice, and since, in a situation where direct action and economic pressure are called for, the justice of the matter has either not been clearly defined by law or the law is not effectively present, there has to be a morality of means applied in every case in which people take it upon themselves to use economic pressures or other forms of force.

Anarchism is generally defined as the political philosophy which holds the state to be undesirable, unnecessary, and harmful ,< ref name =" definition ">

Convolution is similar to cross-correlation.

Similarly, the cross-correlation of and is given by:

This effect is the basis for the code division multiple access ( CDMA ) property of DSSS, which allows multiple transmitters to share the same channel within the limits of the cross-correlation properties of their PN sequences.

Pick two maximum length sequences of the same length such that their absolute cross-correlation is less than or equal to, where is the size of the LFSR used to generate the maximum length sequence ( Gold ' 67 ).

The highest absolute cross-correlation in this set of codes is for even and for odd.

Here, and the and are model parameters with usually set to zero, chosen so that there is no cross-correlation between the real and imaginary parts of:

When a mobile is " searching ", it is attempting to find pilot signals on the network by tuning to particular radio frequencies, and performing a cross-correlation across all possible PN phases.

More precisely, the spatial coherence is the cross-correlation between two points in a wave for all times.

A signature of the late-time ISW is a non-zero cross-correlation function between the galaxy density ( the number of galaxies per square degree ) and the temperature of the CMB, because superclusters gently heat photons, while supervoids gently cool them.

In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them.

For continuous functions, f and g, the cross-correlation is defined as:

Similarly, for discrete functions, the cross-correlation is defined as:

The cross-correlation is similar in nature to the convolution of two functions.

In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero unless the signal is a trivial zero signal.

In probability theory and statistics, correlation is always used to include a standardising factor in such a way that correlations have values between − 1 and + 1, and the term cross-correlation is used for referring to the correlation corr ( X, Y ) between two random variables X and Y, while the " correlation " of a random vector X is considered to be the correlation matrix ( matrix of correlations ) between the scalar elements of X.

If and are two independent random variables with probability density functions f and g, respectively, then the probability density of the difference is formally given by the cross-correlation ( in the signal-processing sense ) ; however this terminology is not used in probability and statistics.

In econometrics, lagged cross-correlation is sometimes referred to as cross-autocorrelation