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In time series analysis and statistics, the cross-correlation of a pair of random process is the correlation between values of the processes at different times, as a function of the two times. Let ( X t , Y t ) {\displaystyle (X_{t},Y_{t})} be a pair of random processes, and t {\displaystyle t} be any point in time ( t {\displaystyle t} may be ...
The Volterra series is a model for non-linear behavior similar to the Taylor series.It differs from the Taylor series in its ability to capture "memory" effects. The Taylor series can be used for approximating the response of a nonlinear system to a given input if the output of the system depends strictly on the input at that particular time.
In statistics, the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag. Let { X t } {\displaystyle \left\{X_{t}\right\}} be a random process, and t {\displaystyle t} be any point in time ( t {\displaystyle t} may be an ...
The circuit shown in the bottom diagram only can model the differential mode. In the top circuit, the voltage doublers, the difference amplifiers, and impedances Z o (s) account for the interaction of the transmission line with the external circuit. This circuit is a useful equivalent for an unbalanced transmission line like a coaxial cable.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
In signal processing, the coherence is a statistic that can be used to examine the relation between two signals or data sets. It is commonly used to estimate the power transfer between input and output of a linear system. If the signals are ergodic, and the system function is linear, it can be used to estimate the causality between the input ...
Scaled correlation between two signals is defined as the average correlation computed across short segments of those signals. First, it is necessary to determine the number of segments K {\displaystyle K} that can fit into the total length T {\displaystyle T} of the signals for a given scale s {\displaystyle s} :
A circuit composed solely of components connected in series is known as a series circuit; likewise, one connected completely in parallel is known as a parallel circuit. Many circuits can be analyzed as a combination of series and parallel circuits, along with other configurations .