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Topic: Autocorrelation function

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	Autocorrelation - Wikipedia, the free encyclopedia
		Autocorrelation is a mathematical tool used frequently in signal processing for analysing functions or series of values, such as time domain signals.
		Autocorrelation is useful for finding repeating patterns in a signal, such as determining the presence of a periodic signal which has been buried under noise, or identifying the fundamental frequency of a signal which doesn't actually contain that frequency component, but implies it with many harmonic frequencies.
		One application of autocorrelation is the measurement of optical spectra and the measurement of very-short-duration light pulses produced by lasers, both using optical autocorrelators.
	en.wikipedia.org /wiki/Autocorrelation (554 words)

	Patent 4456959: Period measurement system
		An autocorrelation function is computed for a value of a phase difference variable over a range determined by a set minimum period and a set maximum periods of one beat, corresponding to a maximum heart rate and a minimum heart rate, respectively.
		The autocorrelation system operates by sampling a heartbeat signal over a suitable sampling period, computing the autocorrelation function of the heartbeat signal on the basis of the sampled data, and measuring the period of the heartbeat signal from the computed autocorrelation function.
		The multiplier 8 and adder 10 compute the autocorrelation function given by equation (3) on the basis of the data stored in the data memory 6, with the result of the computation being stored in a correlation memory 12 that is connected to the adder 10.
	www.freepatentsonline.com /4456959.html (5242 words)

	Lagged Autocorrelation Function (Site not responding. Last check: 2007-11-05)
		The SPSS autocorrelation procedure (ACF) provides both a table of the lagged autocorrelation for each time lag and a graph of the lagged autocorrelations as a function of the lag k.
		If only one or two of the lagged autocorrelations at higher lags are significant, this may not be indicative of a pattern; but if autocorrelations at lags 1 or 2 are statistically significant, then this usually means some pattern is present in the time-series data.
		If the lagged autocorrelation function oscillates (shows a cyclic pattern), this may suggest that a cycle is present in the original time-series data.
	www.runet.edu /~nhashemz/econ521/lagged_autocorrelation_function.htm (312 words)

	Tech Report: HPL-BRIMS-2001-11: Autocorrelation Function of Eigenstates
		Abstract: We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits.
		We obtain an expansion of the autocorrelation function in terms of the correlation length.
		For chaotic systems, the expansion of the autocorrelation function can be used to test quantum ergodicity on different length scales.
	www.hpl.hp.com /techreports/2001/HPL-BRIMS-2001-11.html (119 words)

	Autocorrelation (Site not responding. Last check: 2007-11-05)
		Autocorrelation gives an indication to what degree the time signal f(t) is similar to a displaced (delayed) version of itself as a function of the displacement.
		The average autocorrelation function of periodic signals of period T are also periodic with the same period.
		The autocorrelation of a sine wave is a cosine waveshape [REF10].
	home.hccnet.nl /kees.krijnen/lls/pcs.htm (2128 words)

	Patent 4071903: Autocorrelation function factor generating method and circuitry therefor
		The invention relates to methods and circuitry for generating autocorrelation function factors for electric wave modulation systems, and it particularly pertains to such for delta modulation systems and the like where the resulting electric wave is a data stream of (bivalued) bits.
		However, the autocorrelation function circuitry does not have a source of signal and time delay circuitry reapplying the signal to multiplying circuitry as in the circuitry according to the invention as will be set forth more specifically hereinafter.
		The simplicity of the autocorrelation function factor generating circuitry according to the invention is apparent upon inspection of the functional diagram of FIG.
	www.freepatentsonline.com /4071903.html (3247 words)

	Patent 4512024: Impulse autocorrelation function communications system
		The system of claim 3 wherein said means for autocorrelation detecting comprises first matched filter means for detecting the first of said pair of code mates and second matched filter means for detecting the second of said pair of code mates.
		for all.tau..noteq.0, where.0..sub.a (.tau.) is the autocorrelation function of code a,.0..sub.b (.tau.) is the autocorrelation function of b, and where.tau.=0 is the location of the main lobe.
		The autocorrelation function outputs of the matched filters 34 and 36 are applied to a linear adder 38 which is operable to provide a lobeless output signal.0..sub.T (.tau.) at the IF frequency in accordance with equation (6).
	www.freepatentsonline.com /4512024.html (2877 words)

	Autocorrelation
		In the first case, the mean function is a sine wave whose magnitude is the mean value of the random variable A. In the second case, the mean function is a constant and is equal to zero.
		From a practical perspective, when calculating the autocorrelation function under these conditions, one of the random variables "integrates out", and we need only integrate with respect to one of the random variables.
		From a mathematical perspective, the calculation of this expectation is similar to that of the autocorrelation function and should not present too many new difficulties.
	www.engr.udayton.edu /faculty/mdaniels/htm315/Autocorrelation.htm (2671 words)

	Patent 4158234: Autocorrelation function parameter determination
		Since integral (2) cannot of course be obtained over a infinitely long time, the function.psi.(.tau.) obtained by the autocorrelator is subject to certain errors, which are due to the stochastic character of the physical phenomena from which the signal V(t) is derived.
		The functions P.sub.1 (t) and P.sub.2 (t) are integrated in two identical integrators 65, 66; the results of integration R.sub.1, R.sub.2 are then transmitted to a computer circuit 67 which determines the time constant.tau..sub.e of the exponential autocorrelation function and gives an output signal 68 corresponding to.tau..sub.e.
		The theory shows that the resulting autocorrelation function is identical with the function which would be obtained by using the signal V(t) itself, provided that the amplitude of the function V(t) has a Gaussian statistic distribution in time.
	www.freepatentsonline.com /4158234.html (5425 words)

	"Random Signals and Noise" Java Applet (Site not responding. Last check: 2007-11-05)
		The autocorrelation function of x(n) is defined as r(k)=E[x(n) x(n+k)] and is related to the system impulse response through r(k)=sum_n h(n) h(n+k).
		Use a tapering windows and adjust its parameter L to improve the autocorrelation function estimate.
		The true autocorrelation function for lags between -20 and 20 are shown in the lower left panel.
	users.ece.gatech.edu /~gtz/java/autocorr/notes.html (447 words)

	1.3.5.12. Autocorrelation
		When the autocorrelation is used to detect non-randomness, it is usually only the first (lag 1) autocorrelation that is of interest.
		When the autocorrelation is used to identify an appropriate time series model, the autocorrelations are usually plotted for many lags.
		The heat flow meter data demonstrate the use of autocorrelation in determining if the data are from a random process.
	www.itl.nist.gov /div898/handbook/eda/section3/eda35c.htm (312 words)

	Convolution and Autocorrelation (Site not responding. Last check: 2007-11-05)
		Here the difference between autocorrelation and convolution is illustrated by considering the following function which is a unit ramp cut off at t = 1.
		The proceedure for calculating the autocorrelation function is illustrated by the applet below.
		In the applet f(t) is shown in purple, f(t + tau) in orange, the area to be integrated is shown in green and the autocorrelation in red.
	cnyack.homestead.com /files/aconv/convau1.htm (276 words)

	Autocorrelation of Random Processes
		We will now look at a correlation function that relates a pair of random variables from the same process to the time separations between them, where the argument to this correlation function will be the time difference.
		The first of these correlation functions we will discuss is the autocorrelation, where each of the random variables we will deal with come from the same random process.
		For the second part, you should recall from statistics that the expected value of the square of a function is equal to the variance.
	cnx.rice.edu /content/m10676/latest (1046 words)

	Quasi-elastic Light Scattering
		In this method one sits at a particular scattering angle and measures the temporal autocorrelation function for that particular scattering vector.
		By picking out a particular scattering wavevector, one can measure the intensity of scattered light (which corresponds to the susceptibility) and the autocorrelation function (which corresponds to the lifetime of the fluctuation) and observe both change as a function of temperature.
		Thus, instead of a delta function, at this later time the superparticle is washed out a bit in space, and now each spatial Fourier component has a different amplitude.
	liq-xtal.cwru.edu /scatter.htm (652 words)

	Checking Convergence in MCMC
		The time-series and autocorrelation function plots for parameters such as variable means, covariances, and the worst linear function can be displayed by specifying the TIMEPLOT and ACFPLOT option.
		You can display autocorrelation function plots for the worst linear function, the variable means, variable variances, and covariances of variables.
		The autocorrelations at each lag less than or equal to the specified lag are displayed in the graph.
	support.sas.com /91doc/getDoc/statug.hlp/mi_sect27.htm (1120 words)

	The Autocorrelation Function and Human Influences on Climate -- Tsonis et al. 285 (5427): 495 -- Science
		The Autocorrelation Function and Human Influences on Climate -- Tsonis et al.
		is the Fourier transform of the autocorrelation function r(k).
		use of the autocorrelation function in a hypothesis-testing context.
	www.sciencemag.org /cgi/content/full/285/5427/495a (1140 words)

	New Crack-Imaging Procedure Using Spatial Autocorrelation Function (Site not responding. Last check: 2007-11-05)
		An innovative method of applying a spatial autocorrelation function to analyze pavement image data is presented in this paper.
		One of the major advantages of using a spatial autocorrelation function is its capability of suppressing the noise.
		By calculating the autocorrelation function of the pavement image, we can measure direction and area of the crack under the presence of background noise.
	www.pubs.asce.org /WWWdisplay.cgi?9400612 (170 words)

	Autocorrelation Function and Power Spectrum of Two-State Random Processes Used in Neurite Guidance -- Odde and Buettner ...
		In principle the value of r for the growth phase (A) could be different from that for the shortening phase (B); however, the present analysis only considers the case where they are the same.
		To compactly describe the dynamics of filopodia and microtubules, we derived analytical expressions for the autocorrelation
		3 B, we derived expressions for the autocorrelation function of microtubule
	www.biophysj.org /cgi/content/full/75/3/1189 (3357 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		The series of autocorrelations for a time series at lags 1, 2,...
		A plot of the ACF against the lag is known as the correlogram.
		ACF can be used for several purposes, such as to identify the presence and length of seasonality in a given time series, to identify time-series models for specific situations, and to determine whether the data are stationary.
	morris.wharton.upenn.edu /forecast/data/definitions/autocorrelation%20function.html (62 words)

	Theory (Site not responding. Last check: 2007-11-05)
		The autocorrelation coefficient measures the degree of association, or correlation, between elements in a string of data separated by lag d.
		Autocorrelations are usually computed on the data transformed to natural logarithms, so first transform the data to natural logs, n
		Autocorrelations are frequently plotted as an autocorrelation function or ACF, a histogram with lag d on the x-axis and correlation coefficient r on the y-axis (click here to see an example).
	classes.entom.wsu.edu /526/ACFcalc.htm (390 words)

	Calculation of autocorrelation function (Site not responding. Last check: 2007-11-05)
		Calculation of a (theoretical) autocorrelation function for a normal random discrete white noise filtered by a stationary filter with impulse response given by function h(j), j >0 can be done by using convolution.
		As another exercise, you can try to compute autocorrelation function of a signal at the output of an oscillatory IIR filter whose poles are 0.9888+ 0.0494i and 0.9888- 0.0494i.
		Discrete-time impulse response of such a filter (assuming numerator = 1) is shown on Figure 4, and the result of the convolution computation is shown as blue curve on Figure 5.
	bass.gmu.edu /ececourses/ece499/notes/note2.html (334 words)

	[No title]
		Since idl computes the autocorrelation of a function via the W-K theorem, I computed the autocorrelation explicitly.
		Below is a list of the autocorrelation functions of the elementary functions explored: sine -> cosine cosine -> cosine comb -> comb gaussian -> broader gaussian tophat -> triangular wave/function Observations: For each elementary function I was able to confirm the W-K theorem.
		Namely that the Fourier Transform of the autocorrelation function is equal to the Fourier Power Spectrum.
	astron.berkeley.edu /~ay203/2001/assignments/fourier/fftshuleen.pro (326 words)

	On Variations of Queue Response for Inputs with the Same Mean and Autocorrelation Function
		This paper explores the variations in mean queue length for stationary arrival processes with the same mean and autocorrelation functions, or equivalently, the same mean and power spectrum.
		Results show that the mean queue length can vary substantially for the first type of process, and can vary moderately for the second type of process, as the parameters of the processes are varied, subject to a specified mean and autocorrelation function.
		However, the mean queue lengths for the third type of arrival processes are determined by the input mean and autocorrelation functions.
	www.comsoc.org /net/private/1998/oct/588_06net05-hajek.html (382 words)

	Autocorrelation function (FFT-->power-->inverse FFT) (Site not responding. Last check: 2007-11-05)
		The autocorrelation function is computed by evaluating the FFT of an image, multiplying by its complex conjugate, and computing the inverse FFT of this spectrum.
		If positive this entry specifies the buffer containing the image for which the autocorrelation function is to be evaluated.
		The answer to this question specifies whether the autocorrelation function is to be evaluated in the horizontal direction only (), the vertical direction only (), or both horizontal and vertical directions ().
	www.damtp.cam.ac.uk /user/fdl/people/sd103/digimage/hlpfiles/s2a.htm (141 words)

	AutoCorrelation (JMSL Numerical Library) (Site not responding. Last check: 2007-11-05)
		Computes the sample autocorrelation function of a stationary time series.
		One method (Bartlett 1946) is based on a general asymptotic expression for the variance of the sample autocorrelation coefficient of a stationary time series with independent, identically distributed normal errors.
		A second method (Moran 1947) utilizes an exact formula for the variance of the sample autocorrelation coefficient of a random process with independent, identically distributed normal errors.
	vni.com /products/imsl/jmsl/v30/api/com/imsl/stat/AutoCorrelation.html (527 words)

	[No title]
		Correlation functions: Autocorrelation function: The autocorrelation function Rxx(t) of a random signal X(t) is a measure of how well the future values of X(t) can be predicted based on past measurements.
		It is the Fourier transform of the autocorrelation function.
		In addition, the autocorrelation function approaches the sine wave process as the bandwidth decreases, a conclusion that can easily be drawn using LTI system theory for deterministic systems.
	www.csus.edu /indiv/n/ngw/EEE-243/Corr_Spectral.doc (1354 words)

	The Two Point Angular Autocorrelation Function
		The two point angular autocorrelation function is then the joint probability of finding an object in both of two elements of solid angle placed at an angular separation of
		In practice, the probability can be found by comparing the number of ensemble pairs having a particular separation (in a given separation interval) with the number derived for a random ensemble which contains the same number of directions.
		We can express the function (w) and its uncertainty (dw derived from a consideration of Poisson statistical uncertainties) through the ratio of the number found in the experimental data to the number in the random data (at a particular angular separation and within an angular range) minus one.
	www.atnf.csiro.au /pasa/17_3/clay/paper/node4.html (498 words)

	Session V15 - Classical Fluids.
		In the vicinity of a non-critical surface, critical adsorption is controlled by a surface field h_1 and described by a universal scaling function G(z/\xi,z/l_1) where z/\xi and z/l_1 are dimensionless depths into the bulk critical mixture scaled by the correlation length \xi and a surface field length l_1, respectively.
		We find that \xi_4(t) has a maximum as a function of t, and the value of the maximum increases as temperature is decreased, while the corresponding static correlation length is nearly constant as a function of temperature.
		The former is calculated by the density functional theory, while a mean field theory of hard dumbbells on a lattice is developed for the latter.
	flux.aps.org /meetings/YR01/MAR01/abs/S7650.html (1907 words)

	The Two Point Angular Autocorrelation Function and the Origin of the Highest Energy Cosmic Rays
		The Two Point Angular Autocorrelation Function and the Origin of the Highest Energy Cosmic Rays
		Prior to the availability of data from that experiment, decisions should be made on techniques for the analysis of the directional properties of those data.
		We examine here one possible analysis tool, the two point angular autocorrelation function.
	www.atnf.csiro.au /pasa/17_3/clay/paper (190 words)

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