Analysis of multirate behavior in electronic systems

Doutoramento em Engenharia ElectrotécnicaEsta tese insere-se na área da simulação de circuitos de RF e microondas, e visa o estudo de ferramentas computacionais inovadoras que consigam simular, de forma eficiente, circuitos não lineares e muito heterogéneos, contendo uma estrutura combinada de blocos analógicos de RF e de banda base e blocos digitais, a operar em múltiplas escalas de tempo. Os métodos numéricos propostos nesta tese baseiam-se em estratégias multi-dimensionais, as quais usam múltiplas variáveis temporais definidas em domínios de tempo deformados e não deformados, para lidar, de forma eficaz, com as disparidades existentes entre as diversas escalas de tempo. De modo a poder tirar proveito dos diferentes ritmos de evolução temporal existentes entre correntes e tensões com variação muito rápida (variáveis de estado activas) e correntes e tensões com variação lenta (variáveis de estado latentes), são utilizadas algumas técnicas numéricas avançadas para operar dentro dos espaços multi-dimensionais, como, por exemplo, os algoritmos multi-ritmo de Runge-Kutta, ou o método das linhas. São também apresentadas algumas estratégias de partição dos circuitos, as quais permitem dividir um circuito em sub-circuitos de uma forma completamente automática, em função dos ritmos de evolução das suas variáveis de estado. Para problemas acentuadamente não lineares, são propostos vários métodos inovadores de simulação a operar estritamente no domínio do tempo. Para problemas com não linearidades moderadas é proposto um novo método híbrido frequência-tempo, baseado numa combinação entre a integração passo a passo unidimensional e o método seguidor de envolvente com balanço harmónico. O desempenho dos métodos é testado na simulação de alguns exemplos ilustrativos, com resultados bastante promissores. Uma análise comparativa entre os métodos agora propostos e os métodos actualmente existentes para simulação RF, revela ganhos consideráveis em termos de rapidez de computação.This thesis belongs to the field of RF and microwave circuit simulation, and is intended to discuss some innovative computer-aided design tools especially conceived for the efficient numerical simulation of highly heterogeneous nonlinear wireless communication circuits, combining RF and baseband analog and digital circuitry, operating in multiple time scales. The numerical methods proposed in this thesis are based on multivariate strategies, which use multiple time variables defined in warped and unwarped time domains, for efficiently dealing with the time-scale disparities. In order to benefit from the different rates of variation of slowly varying (latent) and fast-varying (active) currents and voltages (circuits’ state variables), several advanced numerical techniques, such as modern multirate Runge-Kutta algorithms, or the mathematical method of lines, are proposed to operate within the multivariate frameworks. Diverse partitioning strategies are also introduced, which allow the simulator to automatically split the circuits into sub-circuits according to the different time rates of change of their state variables. Novel purely time-domain techniques are addressed for the numerical simulation of circuits presenting strong nonlinearities, while a mixed frequency-time engine, based on a combination of univariate time-step integration with multitime envelope transient harmonic balance, is discussed for circuits operating under moderately nonlinear regimes. Tests performed in illustrative circuit examples with the newly proposed methods revealed very promising results. Indeed, compared to previously available RF tools, significant gains in simulation speed are reported

Simulation of nonlinear systems subject to modulated chirp signals

Purpose The purpose of the paper is to apply a novel technique for the simulation of nonlinear systems subject to modulated chirp signals. Design/methodology/approach The simulation technique is first described and its salient features are presented. Two examples are given to confirm the merits of the method. Findings The results indicate that the method is appropriate for simulating nonlinear systems subject to modulated chirp signals. In particular, the efficiency and accuracy of the method is seen to improve as the chirp frequency increases. In addition, error bounds are given for the method. Originality/value Chirp signals are employed in several important applications such as representing biological signals and in spread spectrum communications. Analysis of systems involving such signals requires accurate, appropriate and effective simulation techniques

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

Accurate sound synthesis of 3D object collisions in interactive virtual scenarios

Questa tesi affronta lo studio di algoritmi efficienti per la sintesi di suoni risultanti dalla collisione di oggetti generici, partendo da una descrizione fisica del problema. L'obiettivo della ricerca e' lo sviluppo di strumenti in grado di aumentare l'accuratezza del feedback uditivo in ambienti di realta' virtuale attraverso un approccio basato sulla fisica, senza il bisogno quindi di far riferimento a suoni pre-registrati. Data la loro versatilita' nel trattare geometrie complesse, i metodi agli elementi finiti (FEM) sono stati scelti per la discretizzazione spaziale di generici risonatori tridimensionali. Le risultanti equazioni discrete sono riarrangiate in modo da disaccoppiare i modi normali del sistema tramite l'utilizzo di tecniche di Analisi e Sintesi Modale. Queste tecniche, infatti, portano convenientemente ad algoritmi computazionalmente efficienti per la sintesi del suono. Implementazioni di esempio di tali algoritmi sono state sviluppate facendo uso solo di software open-source: questo materiale a corredo della tesi permette una migliore riproducibilita' dei risultati di questa tesi da parte di ricercatori aventi una preparazione nel campo della sintesi audio. I risultati originali presenti in questo lavoro includono: i tecniche efficienti basate sulla fisica che aiutano l'implementazione in tempo reale di algoritmi di sintesi del suono su hardware comune; ii un metodo per la gestione efficiente dei dati provenienti da analisi FEM che, assieme ad un modello espressivo per la dissipazione, permette di calcolare l'informazione caratterizzante un oggetto risonante e salvarla in una struttura dati compatta iii una trasformazione nel dominio discreto del tempo su due diverse rappresentazioni nello spazio degli stati di filtri digitali del secondo ordine, che permette il calcolo esatto di variabili derivate come la velocita' e l'energia di un risonatore anche quando semplici realizzazioni a soli poli sono impiegate i un'efficiente realizzazione multirate di un banco parallelo di risonatori, derivata usando una suddivisione con Quadrature-Mirror-Filters (QMF). Confrontata con lavori simili presenti in letteratura, questa realizzazione permette l'uso di eccitazione nonlineare in feedback per un banco di risonatori in multirate: l'idea chiave consiste nello svolgere un cambio di stato adattivo nel banco di risonatori, muovendo i risonatori dalla frequenza di campionamento elevata, usata per il processamento della fase transiente, ad un insieme di sottofrequenze ridotte usate durante l'evoluzione in stato libero del sistema.This thesis investigates efficient algorithms for the synthesis of sounds produced by colliding objects, starting from a physical description of the problem. The objective of this investigation is to provide tools capable of increasing the accuracy of the synthetic auditory feedback in virtual environments through a physics-based approach, hence without the need of pre-recorded sounds. Due to their versatility in dealing with complex geometries, Finite Element Methods (FEM) are chosen for the space-domain discretization of generic three-dimensional resonators. The resulting state-space representations are rearranged so as to decouple the normal modes in the corresponding equations, through the use of Modal Analysis/Synthesis techniques. Such techniques, in fact, conveniently lead to computationally efficient sound synthesis algorithms. The whole mathematical treatment develops until deriving such algorithms. Finally, implementation examples are provided which rely only on open-source software: this companion material guarantees the reproducibility of the results, and can be handled without much effort by most researchers having a background in sound processing. The original results presented in this work include: i efficient physics-based techniques that help implement real-time sound synthesis algorithms on common hardware; ii a method for the efficient management of FEM data which, by working together with an expressive damping model, allows to pre-compute the information characterizing a resonating object and then to store it in a compact data structure; iii a time-domain transformation of the state-space representation of second-order digital filters, allowing for the exact computation of dependent variables such as resonator velocity and energy, even when simple all-pole realizations are used; iv an efficient multirate realization of a parallel bank of resonators, which is derived using a Quadrature-Mirror-Filters (QMF) subdivision. Compared to similar works previously proposed in the literature, this realization allows for the nonlinear feedback excitation of a multirate filter bank: the key idea is to perform an adaptive state change in the resonator bank, by switching the sampling rate of the resonators from a common highest value, used while processing the initial transient of the signals at full bandwidth, to a set of lower values in ways to enable a multirate realization of the same bank during the steady state evolution of the signals

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique