Introduction and review

• We consider the multichannel autoregressive model:
  

  $$y_{n} + A_{1}y_{n-1} + \ldots + A_{p}y_{n-p} = e_{n}$$ (1)

  
  where $\left\{y_{n}\right\}, n=1 \ldots N$ are $(m \times 1)$ vector-valued observations, and $\left\{A_{k}\right\}, k=1 \ldots p$ are $(m \times m)$ matrix-valued model parameters. Though most audio applications involve only scalar observations, some important extensions (e.g. time-variant models) can, under suitable transformation, be addressed within the multichannel framework. Everything proceeds as in the scalar case, except we must be careful with the order of matrix multplications.