A Hessenberg-based input balanced realization for all-pass systems

In this paper, a novel Hessenberg-based input balanced realization for all-pass systems is derived. The expression of roundoff noise gain for this structure is obtained. An Nth order system implemented with a coupled all-pass sub-filters proposed in [18], in which each all-pass filter is realized using our proposed structure, yields a roundoff noise gain of N + 1, smaller than that of the classical optimal roundoff noise statespace realizations. A design example is presented to illustrate the behavior of the proposed structure and to compare it with a class of existing input balanced structures and the classical optimal roundoff noise realizations. It is shown that for the all-pass filters, the proposed structure outperforms the others in terms of minimizing roundoff noise as well as implementation efficiency.