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WIGNERVILLEDIST - Wigner-Ville distribution

Usage

W = wignervilledist(f);
W = wignervilledist(f, g);

Input parameters

f, g Input vector(s)

Output parameters

w Wigner-Ville distribution

Description

wignervilledist(f) computes the Wigner-Ville distribution of the vector f. The Wigner-Ville distribution is computed by

\begin{equation*} W\left( n+1,k+1 \right)\; =\; \sum_{m=0}^{L-1}{R\left( n+1,m+1 \right)e^{-i2\pi mk/L}}, \end{equation*}

where \(R(n,m)\) is the instantaneous correlation matrix given by

\begin{equation*} R\left( n,m \right)\; =\; z\left( n+m \right)\overline{z\left( n-m \right)}, \end{equation*}

where \(m \in {-L/2,\ldots, L/2 - 1}\), and where \(z\) is the analytical representation of \(f\), when \(f\) is real-valued.

wignervilledist(f,g) computes the cross-Wigner-Ville distribution of f and g.

WARNING: The quadratic time-frequency distributions are highly redundant. For an input vector of length L, the quadratic time-frequency distribution will be a \(L \times L\) matrix.