Functions with real poles and zeros

Typically-real Functions with Assigned Zeros

is said to be typically-real of order p, if in (1.1) the coefficients bn are all real and if either (I) f(z) is regular in |a| =S1 and 3/(ei9) changes sign 2p times as z = eie traverses the boundary of the unit circle, or (II) f(z) is regular in | z\ < 1 and if there is a p < 1 such that for each r in p<r<l, $f(reie) changes sign 2p times as z = reie traverses the circle \z\ =r. This set of fun...

Common-acoustic-poles/zeros approximation of head-related transfer functions

Common-acoustic-poles/zeros (CAPZ) approximation is a more efficient way to model head-related transfer functions (HRTF’s). In CAPZ approximation, a group of HRTF’s can share a set of poles but use their own zeros. Previous CAPZ works, such as the Prony, Shanks and iterative prefiltering methods, were all based on the linearized least-square criterion. A new state-space approach, jointly balanc...

Differential operators and entire functions with simple real zeros

Let φ and f be functions in the Laguerre–Pólya class. Write φ(z) = e−αzφ1(z) and f (z) = e−βzf1(z), where φ1 and f1 have genus 0 or 1 and α,β 0. If αβ < 1/4 and φ has infinitely many zeros, then φ(D)f (z) has only simple real zeros, where D denotes differentiation.  2004 Elsevier Inc. All rights reserved.

Minimal Positive Realizations of Transfer Functions with Positive Real Poles

A standard result of linear-system theory states that a SISO rational th-order transfer function always has an th-order realization. In some applications, one is interested in having a realization with nonnegative entries (i.e., a positive system) and it is known that a positive system may not be minimal in the usual sense. In this paper, we give an explicit necessary and sufficient condition f...

Conformal Mappings And Entire Functions With Real Zeros