The autocorrelation function
, when restricted to the domain [LAMBDA], takes its global maximum at [DELTA]x = 0, and this maximum is identical to E I ||[PHI]||[LAMBDA] J.
The results show that the monomodal character of the intensity autocorrelation function
(Figure 2(a)) is lost during the evaporation of the n-heptane and the subsequent redispersion in water of the agarose particle and at least three well-separated components can be identified in the sample.
The result of the normalized autocorrelation function
decreases gradually with the increase in the code delay [tau] from 0 to 1/2 [f.sub.s].
The inverse Fourier transform of the PSD of Figure 3 provides the autocorrelation function
[R.sub.FF] ([[tau]) = [R.sub.UU] ([tau]) of the input u(t).
In order to find out appropriate ARIMA (p,d,q) model, autocorrelation and partial autocorrelation functions
of time series were evaluated and significance of parameter estimates was tested statistically.
Data included in column 8 is used during radio transmission system selection based on the binary sequence analysis while applying the test of hypothesis with zero correlation coefficient between the bit autocorrelation function
of the binary sequence analysed and standard bit autocorrelation function
of binary sequence described in the database.
In the phase space reconstruction, we cannot find the parameter of time delay Tau using the displacement responses directly with the autocorrelation function
method mentioned in Section 3.2, because the displacement responses are less than zero, which will lead the autocorrelation function
css always less than zero.
The chaotic and quasiperiodic behaviors are confirmed in Figure 12 which presents the autocorrelation function
of the outputs x(t), y(t), z(t), and w(t) of the corresponding phase portraits of fractional-order system (8) depicted in Figure 11.
. Capturing the ACF structure of VBR video traffic is actually more challenging because of the fact that VBR traces exhibit both Long-Range Dependent (LRD) and short-range dependent (SRD) properties.
Calculate the autocorrelation function
of x(n) as in Eq.
Similarly, the uncorrelation of x can be proven by observing the shape of the autocorrelation function
. The autocorrelation is a mathematical tool that calculates the correlation between the elements on a sequence of numbers, like x.
I assessed each of the original time series for the presence and form of autocorrelation by examining its autocorrelation function
(ACF) and partial autocorrelation function
(PACF; Chatfield, 1984).