From IIR to FIR Digital MIMO Models: A Constructive Hankel Norm Approximation Method

This paper presents a constructive method to (sub)optimal finite impulse response (FIR) approximation of a given infinite impulse response (IIR) MIMO model. The method minimizes the Hankel norm of approximation error by using the explicit solution of norm-preserve dilation problem. It has the advantage over the existing methods that it provides an explicitly constructive solution and allows the trade-off between the Chebyshev and least square criteria. The lower and upper bounds on the H2and H∞norms of approximation error are given. The algorithm for approximating non-causal IIR filters by causal FIR filters is also formulated and solved. The effectiveness and properties of the proposed algorithm are demonstrated through two examples.