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The reason () is called the spectral correlation density function is that it equals the limit, as filter bandwidth approaches zero, of the expected value of the product of the output of a one-sided bandpass filter with center frequency + / and the conjugate of the output of another one-sided bandpass filter with center frequency /, with both ...
Similar to the Barker codes are the complementary sequences, which cancel sidelobes exactly when summed; the even-length Barker code pairs are also complementary pairs. There is a simple constructive method to create arbitrarily long complementary sequences.
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix. This is a matrix such that Had ( x ) = x ⋅ G {\displaystyle {\text{Had}}(x)=x\cdot G} holds for all x ∈ { 0 , 1 } k {\displaystyle x\in \{0,1\}^{k}} , where the message x {\displaystyle x} is viewed as a row vector and the vector-matrix product ...
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [ a ] The variables may be two columns of a given data set of observations, often called a sample , or two components of a multivariate random variable with a known distribution .
In the analysis of data, a correlogram is a chart of correlation statistics. For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram. If cross-correlation is plotted, the result is called a cross-correlogram.
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.
Convergent cross mapping (CCM) is a statistical test for a cause-and-effect relationship between two variables that, like the Granger causality test, seeks to resolve the problem that correlation does not imply causation. [1]
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. [1] If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an ...