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Scilabヘルプ >> Signal Processing > Correlation Convolution > hank

hank

共分散からハンケル行列を得る

呼び出し手順

hk =hank(m, n, cov)

引数

m

ブロック行の数

n

ブロック列の数

cov

共分散の系列; 次のように指定します :[R0 R1 R2...Rk]

hk

ハンケル行列の計算値

説明

この関数は,ベクトル過程の共分散系列から 大きさ(m*d,n*d)のハンケル行列を構築します. より正確には以下となります:

この関数は,ベクトル過程の共分散系列から 大きさ(m*d,n*d)のハンケル行列を作成します. より正しくは:

\mathrm{hank}(m, n, [R_0, R_1, R_2, \ldots])=m\mbox{ blocks}\left\{\vphantom{\begin{matrix}R_0\cr R_1\cr R_2\cr\vdots\end{matrix}}\right.\left(\vphantom{\begin{matrix}R_0\cr R_1\cr R_2\cr\vdots\end{matrix}}\right.\overbrace{\begin{matrix}R_0 & R_1 & R_2 & \cdots\cr R_1 & R_2 & \cdots &\cr R_2 & \cdots &&\cr \vdots&&&\cr\end{matrix}}^{n \mbox{ blocks}}\left.\vphantom{\begin{matrix}R_0\cr R_1\cr R_2\cr\vdots\end{matrix}}\right)

//Example of how to use the hank macro for

            //building a Hankel matrix from multidimensional

            //data (covariance or Markov parameters e.g.)

            //

            //This is used e.g. in the solution of normal equations

            //by classical identification methods (Instrumental Variables e.g.)

            //

            //1)let's generate the multidimensional data under the form :

            //  C=[c_0 c_1 c_2 .... c_n]

            //where each bloc c_k is a d-dimensional matrix (e.g. the k-th correlation

            //of a d-dimensional stochastic process X(t) [c_k = E(X(t) X'(t+k)], '

            //being the transposition in scilab)

            //

            //we take here d=2 and n=64

            c = rand(2, 2 * 64)

            //generate the hankel matrix H (with 4 bloc-rows and 5 bloc-columns)

            //from the data in c

            H = hank(4, 5, c);

参照

  • toeplitz — Toeplitz matrix (chosen constant diagonal bands)
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Last updated:
Thu Feb 14 15:02:10 CET 2019