5.3.6 音源定位用相関行列ファイル

マイク数を $M$，入力信号の周波数解析後の周波数ビン数を $N$ とすると， 相関行列は $M$ 次の複素正方行列で，周波数ビン毎に $N$ 個演算される． $n$番目の周波数ビン ($1 \leq n \leq N$) の相関行列 $\boldsymbol {R}(n)$ を以下で表すとする．

 $\displaystyle \boldsymbol{R}(n) = \left[ \begin{array}{ccc} r_{11}(n) & \cdots & r_{1M}(n) \\ \vdots & \ddots & \vdots \\ r_{M1}(n) & \cdots & r_{MM}(n)\\ \end{array} \right]$ (1)

ここで，$r_{11}(n), \cdots , r_{MM}(n)$ は複素数である．

 $\displaystyle \begin{array}{cccccccc} \textrm{Re}[r_{11}(1)] & \textrm{Re}[r_{12}(1)] & \cdots & \textrm{Re}[r_{1M}(1)] & \textrm{Re}[r_{21}(1)] & \textrm{Re}[r_{22}(1)]& \cdots & \textrm{Re}[r_{MM}(1)]\\ \textrm{Re}[r_{11}(2)] & \textrm{Re}[r_{12}(2)] & \cdots & \textrm{Re}[r_{1M}(2)] & \textrm{Re}[r_{21}(2)] & \textrm{Re}[r_{22}(2)]& \cdots & \textrm{Re}[r_{MM}(2)]\\ \textrm{Re}[r_{11}(N)] & \textrm{Re}[r_{12}(N)] & \cdots & \textrm{Re}[r_{1M}(N)] & \textrm{Re}[r_{21}(N)] & \textrm{Re}[r_{22}(N)]& \cdots & \textrm{Re}[r_{MM}(N)]\\ \end{array} \nonumber$

 $\displaystyle \begin{array}{cccccccc} \textrm{Im}[r_{11}(1)] & \textrm{Im}[r_{12}(1)] & \cdots & \textrm{Im}[r_{1M}(1)] & \textrm{Im}[r_{21}(1)] & \textrm{Im}[r_{22}(1)] & \cdots & \textrm{Im}[r_{MM}(1)]\\ \textrm{Im}[r_{11}(2)] & \textrm{Im}[r_{12}(2)] & \cdots & \textrm{Im}[r_{1M}(2)] & \textrm{Im}[r_{21}(2)] & \textrm{Im}[r_{22}(2)] & \cdots & \textrm{Im}[r_{MM}(2)]\\ \textrm{Im}[r_{11}(N)] & \textrm{Im}[r_{12}(N)] & \cdots & \textrm{Im}[r_{1M}(N)] & \textrm{Im}[r_{21}(N)] & \textrm{Im}[r_{22}(N)] & \cdots & \textrm{Im}[r_{MM}(N)]\\ \end{array} \nonumber$