Immittance- versus scattering-domain fast algorithms for non-Hermitian Toeplitz and quasi-Toeplitz matrices

AbstractThe classical algorithms of Schur and Levinson are efficient procedures to solve sets of Hermitian Toeplitz linear equations or to invert the corresponding coefficient matrices. They propagate pairs of variables that may describe incident and scattered waves in an associated cascade-of-layered-media model, and thus they can be viewed as scattering-domain algorithms. It was recently found that a certain transformation of these variables followed by a change from two-term to three-term recursions results in reduction in computational complexity in the abovementioned algorithms roughly by a factor of two. The ratio of such pairs of transformed variables can be interpreted in the above layered-media model as an impedance or admittance; hence the name immittance-domain variables. This paper provides extensions for previous immittance Schur and Levinson algorithms from Hermitian to non-Hermitian matrices. It considers both Toeplitz and quasi-Toeplitz matrices (matrices with certain “hidden” Toeplitz structure) and compares two- and three-term recursion algorithms in the two domains. The comparison reveals that for non-Hermitian matrices the algorithms are equally efficient in both domains. This observation adds new comprehension to the source and value of algorithms in the immittance domain. The immittance algorithms, like the scattering algorithms, exploit the (quasi-)Toeplitz structure to produce fast algorithms. However, unlike the scattering algorithms, they can respond also to symmetry of the underlying matrix when such extra structure is present, and yield algorithms with improved efficiency

Linear predictive modelling of speech : constraints and line spectrum pair decomposition

In an exploration of the spectral modelling of speech, this thesis presents theory and applications of constrained linear predictive (LP) models. Spectral models are essential in many applications of speech technology, such as speech coding, synthesis and recognition. At present, the prevailing approach in speech spectral modelling is linear prediction. In speech coding, spectral models obtained by LP are typically quantised using a polynomial transform called the Line Spectrum Pair (LSP) decomposition. An inherent drawback of conventional LP is its inability to include speech specific a priori information in the modelling process. This thesis, in contrast, presents different constraints applied to LP models, which are then shown to have relevant properties with respect to root loci of the model in its all-pole form. Namely, we show that LSP polynomials correspond to time domain constraints that force the roots of the model to the unit circle. Furthermore, this result is used in the development of advanced spectral models of speech that are represented by stable all-pole filters. Moreover, the theoretical results also include a generic framework for constrained linear predictive models in matrix notation. For these models, we derive sufficient criteria for stability of their all-pole form. Such models can be used to include a priori information in the generation of any application specific, linear predictive model. As a side result, we present a matrix decomposition rule for Toeplitz and Hankel matrices.reviewe

Discrete matrix Schrodinger equation equivalents of discrete two-component matrix wave systems

Multichannel discrete lossless two-component wave systems describe physical scattering for multiple coupled transmission lines, for elastic media, and for electromagnetic wave propagation in layered media. Such a wave system is transformed into an equivalent discrete matrix Schrodinger equation that includes the effects of transmission losses and transmission scattering. These effects are not included in the continuous Schrodinger equation, so that discretisation of the latter omits significant effects. Applications include fast algorithms for synthesis and inversion of the reflection responses of multichannel scattering media. These algorithms require roughly half as many matrix multiplications as previous algorithms that employ the multichannel two-component wave system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49091/2/ipv5i3p425.pd

On the synthesis of a class of 2-D acausal lossless digital filters

Cover title.Includes bibliographical references.Sankar Basu

Dielectric mixtures -- electrical properties and modeling

In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.Comment: 40 pages 12 figures, to be appear in IEEE Trans. on Dielectric

Amélioration de codecs audio standardisés avec maintien de l'interopérabilité

Résumé : L’audio numérique s’est déployé de façon phénoménale au cours des dernières décennies, notamment grâce à l’établissement de standards internationaux. En revanche, l’imposition de normes introduit forcément une certaine rigidité qui peut constituer un frein à l’amélioration des technologies déjà déployées et pousser vers une multiplication de nouveaux standards. Cette thèse établit que les codecs existants peuvent être davantage valorisés en améliorant leur qualité ou leur débit, même à l’intérieur du cadre rigide posé par les standards établis. Trois volets sont étudiés, soit le rehaussement à l’encodeur, au décodeur et au niveau du train binaire. Dans tous les cas, la compatibilité est préservée avec les éléments existants. Ainsi, il est démontré que le signal audio peut être amélioré au décodeur sans transmettre de nouvelles informations, qu’un encodeur peut produire un signal amélioré sans ajout au décodeur et qu’un train binaire peut être mieux optimisé pour une nouvelle application. En particulier, cette thèse démontre que même un standard déployé depuis plusieurs décennies comme le G.711 a le potentiel d’être significativement amélioré à postériori, servant même de cœur à un nouveau standard de codage par couches qui devait préserver cette compatibilité. Ensuite, les travaux menés mettent en lumière que la qualité subjective et même objective d’un décodeur AAC (Advanced Audio Coding) peut être améliorée sans l’ajout d’information supplémentaire de la part de l’encodeur. Ces résultats ouvrent la voie à davantage de recherches sur les traitements qui exploitent une connaissance des limites des modèles de codage employés. Enfin, cette thèse établit que le train binaire à débit fixe de l’AMR WB+ (Extended Adaptive Multi-Rate Wideband) peut être compressé davantage pour le cas des applications à débit variable. Cela démontre qu’il est profitable d’adapter un codec au contexte dans lequel il est employé.Abstract : Digital audio applications have grown exponentially during the last decades, in good part because of the establishment of international standards. However, imposing such norms necessarily introduces hurdles that can impede the improvement of technologies that have already been deployed, potentially leading to a proliferation of new standards. This thesis shows that existent coders can be better exploited by improving their quality or their bitrate, even within the rigid constraints posed by established standards. Three aspects are studied, being the enhancement of the encoder, the decoder and the bit stream. In every case, the compatibility with the other elements of the existent coder is maintained. Thus, it is shown that the audio signal can be improved at the decoder without transmitting new information, that an encoder can produce an improved signal without modifying its decoder, and that a bit stream can be optimized for a new application. In particular, this thesis shows that even a standard like G.711, which has been deployed for decades, has the potential to be significantly improved after the fact. This contribution has even served as the core for a new standard embedded coder that had to maintain that compatibility. It is also shown that the subjective and objective audio quality of the AAC (Advanced Audio Coding) decoder can be improved, without adding any extra information from the encoder, by better exploiting the knowledge of the coder model’s limitations. Finally, it is shown that the fixed rate bit stream of the AMR-WB+ (Extended Adaptive Multi-Rate Wideband) can be compressed more efficiently when considering a variable bit rate scenario, showing the need to adapt a coder to its use case

Media gateway utilizando um GPU

Mestrado em Engenharia de Computadores e Telemátic

Compensation technique for nonlinear distortion in RF circuits for multi-standard wireless systems

Recent technological advances in the RF and wireless industry has led to the design requirement of more sophisticated devices which can meet stringent specifications of bandwidth, data rate and throughput. These devices are required to be extremely sensitive and hence any external interference from other systems can severely affect the device and the output. This thesis introduces the existing problem in nonlinear components in a multi-standard wireless system due to interfering signals and suggests potential solution to the problem. Advances in RF and wireless systems with emerging new communication standards have made reconfigurablility and tunability a very viable option. RF transceivers are optimised for multi-standard operation, where one band of frequency can act as an interfering signal to the other band. Due to the presence of nonlinear circuits in the transceiver chains such as power amplifiers, reconfigurable and tunable filters and modulators, these interfering signals produce nonlinear distortion products which can deform the output signal considerably. Hence it becomes necessary to block these interfering signals using special components. The main objective of this thesis is to analyse and experimentally verify the nonlinear distortions in various RF circuits such as reconfigurable and tunable filters and devise ways to minimize the overall nonlinear distortion in the presence of other interfering signals. Reconfigurbality and tunablity in filters can be achieved using components such as varactor diodes, PIN diodes and optical switches. Nonlinear distortions in such components are measured using different signals and results noted. The compensation method developed to minimize nonlinear distortions in RF circuits caused due to interfering signals is explored thoroughly in this thesis. Compensation method used involves the design of novel microstrip bandstop filters which can block the interfering signals and hence give a clean output spectrum at the final stage. Recent years have seen the emergence of electronic band gap technology which has “band gap” properties meaning that a bandstop response is seen within particular range of frequency. This concept was utilised in the design of several novel bandstop filters using defected microstrip structure. Novel tunable bandstop filters has been introduced in order to block the unwanted signal. Fixed single-band and dual-band filters using DMS were fabricated with excellent achieved results. These filters were further extended to tunable structures. A dual-band tunable filter with miniaturized size was developed and designed. The designed filters were further used in the compensation technique where different scenarios showing the effect of interfering signals in wireless transceiver were described. Mathematical analysis proved the validation of the use of a bandstop filter as an inter-stage component. Distortion improvements of around 10dB have been experimentally verified using a power amplifier as device under test. Further experimental verification was carried out with a transmitter which included reconfigurable RF filters and power amplifier where an improvement of 15dB was achieved