離散時間系IIRフィルタの最適FIR近似

抄録

FIR (Finite Impulse Response) filters are preparred to IIR (Imfinite Impulse Response) filters, because of their stabilities or realizations and so on. This paper supposes a new method to approximate an IIR filter by an FIR filter, which directly deal with optimal approximation with respect to the H^∞ error norm. There is an elegant way called Nehari Shuffle which makes use of what is called Nehari extention theorem, but it dosen’t necessarily give an optimal approximation with respect to H^∞ norm. In cotrast to it, we regard this optimal approximated problem as the minimization problem of the error between a IIR filter and a FIR filter with respect to H^∞ norm, and show this problem reduces an LMI (Linear Matrix Inequality). We also introduce this problem depends on the choice of weighting functions. Finally, we show them with numerical examples.