Improved LBR two-pair extraction methods for low sensitivity digital filter realizations

In this paper, we present two improved lossless bounded-real (LBR) two-pair extraction methods using an allpass input function, which significantly reduce roundoff errors during the extraction process and reduce the amount of computation nearly to a half. Both methods are based on the induced allpass transfer function from the given BR function, which is obtained by replacing the value of the terminating multiplier with 1 or -1. The first method is an LBR two-pair extraction based directly on the allpass input function induced from the given input transfer function. The second extraction method is based on two new real polynomials obtained by further decomposing the induced allpass input function. Even with two polynomials, the involved polynomial division and parameter calculation are simpler in the second method. Consequently, numerical errors are further reduced in the second method. The benefits of employing the two improved methods are confirmed through simulation examples.