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    Advances in Wave Digital Modeling of Linear and Nonlinear Systems: A Summary

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    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

    Discrete-Time Circuital Modeling of Hysteretic Piezo-Actuated MEMS Loudspeakers for In-Ear Applications

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    Piezoelectrically actuated micro-electromechanical systems (MEMS) loudspeakers have experienced significant advancements in recent years, achieving acoustic performance for in-ear applications comparable with traditional electrodynamic microspeakers. Despite their advantages in compactness, power efficiency, and ease of integration, these devices are limited by nonlinear hysteretic effects inherent to piezoelectric transduction, which often lead to undesirable distortion. Accurate and computationally efficient models are crucial for enabling digital signal processing (DSP) precompensation algorithms to address this challenge. While well-established nonlinear lumped-element models of electrodynamic loudspeakers have supported DSP techniques for equalization and linearization, the lack of analogous models for MEMS loudspeakers has constrained their broader application. This article presents a nonlinear discrete-time circuital model for a piezo-actuated MEMS loudspeaker designed for in-ear applications. The proposed model integrates two key processing components: a neural network (NN)-based block that accurately captures the nonlinear hysteretic behavior of piezoelectric transduction, and a linear circuit-equivalent block that represents the loudspeaker's vibration and acoustic environment. The discrete-time implementation of the model, including a wave digital filter (WDF) realization of the circuit-equivalent block, enables efficient and accurate simulation of nonlinear hysteretic dynamics under arbitrary input signals. Validation against experimental data-including time-domain pressure waveforms, frequency-domain sound pressure level (SPL), and total harmonic distortion (THD)-demonstrates the model's accuracy and effectiveness across a wide range of operating conditions

    Nullor-Based Inversion of MIMO Circuital Systems

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    Nullors have already demonstrated their efficacy in designing the inverse of a given circuital system in the Single-Input Single-Output (SISO) case. These inverse systems have found diverse applications, ranging from analog electronics, particularly in chaos synchronization, to digital signal processing, for the development of transducer virtualization algorithms. In this brief, we extend the nullor-based circuit inversion approach to the Multiple-Input Multiple-Output (MIMO) case. In particular, we generalize Leuciuc's theorem, originally applicable to SISO systems, to the class of MIMO circuital systems whose input and output signals share the same vector space dimension. The validity of the presented theoretical result is verified in different linear and nonlinear application scenarios
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