Rafael Dias de Paiva
This thesis addresses the use of circuit modeling techniques in audio. Circuit modeling has a wide range of applications in audio, including real-time models of analog electronic audio equipment and the use of physical analogies for understanding and simulating musical instru-ments. Modeling of analog audio equipment is an important topic in audio signal processing. It enables the development of musical software that is capable of simulating rare vintage equip-ment at a low cost. This type of software can be embedded in portable electronic equipment, in mobile phones or tablets, or in computers.
This thesis presents novel models of analog audio equipment used with guitars. It presents a nonlinear audio-transformer model which is used for real-time emulation of vacuum-tube guitar amplifiers. This model has shown that some audio transformers have nonlinear effects for input signals with frequencies below 100 Hz. A new wave-digital model for operational amplifiers is proposed, which is used to simulate a wide class of guitar distortion circuits. The same distortion circuits were modeled with a novel method based on nonlinear system identi-fication, which is enhanced using principal component analysis (PCA) for reduced complexity. It was shown that the proposed method reduces the complexity of the polynomial-Hammer-stein model obtained with the swept-sine technique by 66 %. Additionally, electromagnetic pickups were analyzed and modeled, leading to new pickup-mixing and nonlinearity models and to a better understanding on the effects of guitar pickup and cable interaction.
This thesis has also presented how to use physical analogies for audio synthesis. Electro-acous-tic analogies were used in order to obtain a model of connected Helmholtz resonators, resulting in the so called Helmholtz resonator tree. This model was implemented using wave-digital filters, which enables musical synthesis using physical descriptors that are intuitive also for non-technical users. This thesis includes contributions for the application of circuit modeling techniques in audio. The audio transformer, electromagnetic pickup, and effect-box modeling developments are important for building real-time systems for audio effects and for preserving the heritage of vintage analog equipment. Finally, the electro-acoustic analogies presented show that circuit modeling can be used for abstract musical synthesis, where a virtual instrument can be excited in different manners yielding interesting timbre variations