An estimation method of the pairing and ordering for IIR digital filters with low roundoff noise

Abstract

AbstractThis paper considers the IIR cascade digital filter based on the fixed‐point arithmetic, and presents a method for estimation of the optimal pairing and ordering to minimize the output roundoff noise. In the proposed method, the computational complexity required in the estimation is reduced by considering only the pole frequencies of the transfer function in the evaluation. In the scaling of each branch node, the general L2 ‐ and L∞‐norms are assumed.The proposed method is compared with the methods of Jackson, Lee and Liu‐Peled which are used frequently in practice. The four methods are applied actually to two kinds of filters, and the computational complexities are compared. It is shown as a result that the proposed method requires almost the same computational complexity as those of Jackson and Lee from the lower‐order to higher‐order filters, and realizes the pairing and ordering with smaller output roundoff noise. It is shown also in general that the pairing has a larger effect on the normalized output roundoff noise than the ordering.