advances in wave digital modeling of linear and nonlinear systems a summary

This brief summarizes some of the main research results that I obtained during the three years, ranging from November 2015 to October 2018, as a Ph.D. student at Politecnico di Milano under the supervision of Professor Augusto Sarti, and that are contained in my doctoral dissertation, entitled "Advances in Wave Digital Modeling of Linear and Nonlinear Systems". The thesis provides contributions to all the main aspects of Wave Digital (WD) modeling of lumped systems: it introduces generalized definitions of wave variables; it presents novel WD models of one- and multi-port linear and nonlinear circuit elements; it discusses systematic techniques for the WD implementation of arbitrary connection networks and it describes a novel iterative method for the implementation of circuits with multiple nonlinear elements. Though WD methods usually focus on the discrete-time implementation of analog audio circuits; the methodologies addressed in the thesis are general enough as to be applicable to whatever system that can be described by an equivalent electric circuit

Steerable circular differential microphone arrays

An efficient continuous beam steering method, applicable to differential microphones of any order, has been recently developed. Given two identical reference beams, pointing in two different directions, the method allows to derive a beam of nearly constant shape continuously steerable between those two directions. In this paper, the steering method is applied to robust Differential Microphone Arrays (DMAs) characterized by uniform circular array geometries. In particular, a generalized filter performing the steering operation is defined. The definition of such a filter enables the derivation of closed-form formulas for computing the white noise gain and the directivity factor of the designed steerable differential beamformers for any frequency of interest. A study on the shape invariance of the steered beams is conducted. Applications of the steering approach to first-, second- and third-order robust circular DMAs are presented