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For a Gaussian time profile, the autocorrelation width is longer than the width of the intensity, and it is 1.54 longer in the case of a hyperbolic secant squared (sech 2) pulse. This numerical factor, which depends on the shape of the pulse, is sometimes called the deconvolution factor. If this factor is known, or assumed, the time duration ...
The traditional test for the presence of first-order autocorrelation is the Durbin–Watson statistic or, if the explanatory variables include a lagged dependent variable, Durbin's h statistic. The Durbin-Watson can be linearly mapped however to the Pearson correlation between values and their lags. [ 12 ]
Calibration Factor-- the factor to convert real-time to pulse delay time when viewing the output of the autocorrelator.One example of this would be 30 ps/ms in the Coherent Model FR-103 scanning autocorrelator, which suggests that a 30 ps pulse autocorrelation width would produce a 1 ms FWHM trace when viewed on an oscilloscope.
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum ...
Often a Gaussian light source is chaotic and consequently, Figure 3. The second order coherence for stellar light as measured in the Hanbury Brown and Twiss experiment as a function of the time delay introduced between the signals τ / τ 0 {\displaystyle \tau /\tau _{0}} , where τ 0 {\displaystyle \tau _{0}} is the coherence length.
When these assumptions are satisfied, the following covariance matrix K applies for the 1D profile parameters , , and under i.i.d. Gaussian noise and under Poisson noise: [9] = , = , where is the width of the pixels used to sample the function, is the quantum efficiency of the detector, and indicates the standard deviation of the measurement noise.
where N is the sample size, z is the quantile function of the standard normal distribution and α is the significance level. In this case, the confidence bands have fixed width that depends on the sample size. 2. Correlograms are also used in the model identification stage for fitting ARIMA models.
In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation function) or 1/f noise.