Elimination of delay-free loops in discrete-time models of nonlinear acoustic systems

• Published in: IEEE transactions on speech and audio processing Vol. 8; no. 5; pp. 597 - 605
• Main Authors: Borin, G., De Poli, G., Rocchesso, D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2000; Institute of Electrical and Electronics Engineers
• Subjects: Acoustics; Applied sciences; Boring; Circuit simulation; Circuit synthesis; Computational modeling; Delay; Differential equations; Digital filters; Exact sciences and technology; Information, signal and communications theory; Mathematical analysis; Mathematical models; Nonlinear acoustics; Nonlinear circuits; Nonlinear dynamical systems; Nonlinear equations; Nonlinearity; Sampling; Signal processing; Speech processing; Telecommunications and information theory; Transformations; Initial condition; Differential equation; Acoustics; Non linear system; Modeling; Delay; System decomposition; Sound pressure; Non linear circuit; Time dependence; Linear equation; Sampling rate; Discrete time; Nonlinearity; Sampling
• ISSN: 1063-6676; 1558-2353
• DOI: 10.1109/89.861380

Nonlinear acoustic systems are often described by means of nonlinear maps acting as instantaneous constraints on the solutions of a system of linear differential equations. This description leads to discrete-time models exhibiting noncomputable loops. We present a solution to this computability problem by means of geometrical transformation of the nonlinearities and algebraic transformation of the time-dependent equations. The proposed solution leads to stable and accurate simulations even at relatively low sampling rates.