## Polynomial Matrix Eigenvalue Decomposition Techniques for Multichannel Signal Processing (2018)

Advanced Algorithms for Polynomial Matrix Eigenvalue Decomposition

Matrix factorisations such as the eigen- (EVD) or singular value decomposition (SVD) offer optimality in often various senses to many narrowband signal processing algorithms. For broadband problems, where quantities such as MIMO transfer functions or cross spectral density matrices are conveniently described by polynomial matrices, such narrowband factorisations are suboptimal at best. To extend the utility of EVD and SVD to the broadband case, polynomial matrix factorisations have gained momen- tum over the past decade, and a number of iterative algorithms for particularly the polynomial matrix EVD (PEVD) have emerged. Existing iterative PEVD algorithms produce factorisations that are computationally costly (i) to calculate and (ii) to apply. For the former, iterative algorithms at every step eliminate off-diagonal energy, but this can be a slow process. For the latter, the polynomial order of the resulting factors, directly impacting on the implementa- ...

Corr, Jamie — University of Strathclyde

Algorithms and Techniques for Polynomial Matrix Decompositions

The concept of polynomial matrices is introduced and the potential application of polynomial matrix decompositions is discussed within the general context of multi-channel digital signal processing. A recently developed technique, known as the second order sequential rotation algorithm (SBR2), for performing the eigenvalue decomposition of a para-Hermitian polynomial matrix (PEVD) is presented. The potential benefit of using the SBR2 algorithm to impose strong decorrelation on the signals received by a broadband sensor array is demonstrated by means of a suitable numerical simulation. This demonstrates how the polynomial matrices produced as a result of the PEVD can be of unnecessarily high order. This is undesirable for many practical applications and slows down the iterative computational procedure. An effective truncation technique for controlling the growth in order of these polynomial matrices is proposed. Depending on the choice of truncation parameters, it provides ...

Foster, Joanne — Cardiff University

Broadband angle of arrival estimation using polynomial matrix decompositions

This thesis is concerned with the problem of broadband angle of arrival (AoA) estimation for sensor arrays. There is a rich theory of narrowband solutions to the AoA problem, which typically involves the covariance matrix of the received data and matrix factorisations such as the eigenvalue decomposition (EVD) to reach optimality in various senses. For broadband arrays, such as found in sonar, acoustics or other applications where signals do not fulfil the narrowband assumption, working with phase shifts between different signals — as sufficient in the narrowband case — does not suffice and explicit lags need to be taken into account. The required space-time covariance matrix of the data now has a lag dimension, and classical solutions such as those based on the EVD are no longer directly applicable. There are a number of existing broadband AoA techniques, which are ...

Alrmah, Mohamed Abubaker — University of Strathclyde

Polynomial Matrix Decompositions and Paraunitary Filter Banks

There are an increasing number of problems that can be solved using paraunitary filter banks. The design of optimal orthonormal filter banks for the efficient coding of signals has received considerable interest over the years. In contrast, very little attention has been given to the problem of constructing paraunitary matrices for the purpose of broadband signal subspace estimation. This thesis begins by relating these two areas of research. A frequency-domain method of diagonalising parahermitian polynomial matrices is proposed and shown to have fundamental limitations. Then the thesis focuses on the development of a novel time-domain technique that extends the eigenvalue decomposition to polynomial matrices, referred to as the second order sequential best rotation (SBR2) algorithm. This technique imposes strong decorrelation on its input signals by applying a sequence of elementary paraunitary matrices which constitutes a generalisation of the classical Jacobi ...

Redif, Soydan — University of Southampton

MIMO instantaneous blind idenfitication and separation based on arbitrary order

This thesis is concerned with three closely related problems. The first one is called Multiple-Input Multiple-Output (MIMO) Instantaneous Blind Identification, which we denote by MIBI. In this problem a number of mutually statistically independent source signals are mixed by a MIMO instantaneous mixing system and only the mixed signals are observed, i.e. both the mixing system and the original sources are unknown or ¡blind¢. The goal of MIBI is to identify the MIMO system from the observed mixtures of the source signals only. The second problem is called Instantaneous Blind Signal Separation (IBSS) and deals with recovering mutually statistically independent source signals from their observed instantaneous mixtures only. The observation model and assumptions on the signals and mixing system are the same as those of MIBI. However, the main purpose of IBSS is the estimation of the source signals, whereas ...

van de Laar, Jakob — T.U. Eindhoven

Subspace-based exponential data fitting using linear and multilinear algebra

The exponentially damped sinusoidal (EDS) model arises in numerous signal processing applications. It is therefore of great interest to have methods able to estimate the parameters of such a model in the single-channel as well as in the multi-channel case. Because such a model naturally lends itself to subspace representation, powerful matrix approaches like HTLS in the single-channel case, HTLSstack in the multi-channel case and HTLSDstack in the decimative case have been developed to estimate the parameters of the underlying EDS model. They basically consist in stacking the signal in Hankel (single-channel) or block Hankel (multi- channel) data matrices. Then, the signal subspace is estimated by means of the singular value decomposition (SVD). The parameters of the model, namely the amplitudes, the phases, the damping factors, and the frequencies, are estimated from this subspace. Note that the sample covariance matrix ...

Papy, Jean-Michel — Katholieke Universiteit Leuven

Feedback Delay Networks in Artificial Reverberation and Reverberation Enhancement

In today's audio production and reproduction as well as in music performance practices it has become common practice to alter reverberation artificially through electronics or electro-acoustics. For music productions, radio plays, and movie soundtracks, the sound is often captured in small studio spaces with little to no reverberation to save real estate and to ensure a controlled environment such that the artistically intended spatial impression can be added during post-production. Spatial sound reproduction systems require flexible adjustment of artificial reverberation to the diffuse sound portion to help the reconstruction of the spatial impression. Many modern performance spaces are multi-purpose, and the reverberation needs to be adjustable to the desired performance style. Employing electro-acoustic feedback, also known as Reverberation Enhancement Systems (RESs), it is possible to extend the physical to the desired reverberation. These examples demonstrate a wide range of applications ...

Schlecht, Sebastian Jiro — Friedrich-Alexander-Universität Erlangen-Nürnberg

Unsupervised Models for White Matter Fiber-Bundles Analysis in Multiple Sclerosis

Diffusion Magnetic Resonance Imaging (dMRI) is a meaningful technique for white matter (WM) fiber-tracking and microstructural characterization of axonal/neuronal integrity and connectivity. By measuring water molecules motion in the three directions of space, numerous parametric maps can be reconstructed. Among these, fractional anisotropy (FA), mean diffusivity (MD), and axial (λa) and radial (λr) diffusivities have extensively been used to investigate brain diseases. Overall, these findings demonstrated that WM and grey matter (GM) tissues are subjected to numerous microstructural alterations in multiple sclerosis (MS). However, it remains unclear whether these tissue alterations result from global processes, such as inflammatory cascades and/or neurodegenerative mechanisms, or local inflammatory and/or demyelinating lesions. Furthermore, these pathological events may occur along afferent or afferent WM fiber pathways, leading to antero- or retrograde degeneration. Thus, for a better understanding of MS pathological processes like its spatial and ...

Stamile, Claudio — Université Claude Bernard Lyon 1, KU Leuven

Advanced Multi-Dimensional Signal Processing for Wireless Systems

The thriving development of wireless communications calls for innovative and advanced signal processing techniques targeting at an enhanced performance in terms of reliability, throughput, robustness, efficiency, flexibility, etc.. This thesis addresses such a compelling demand and presents new and intriguing progress towards fulfilling it. We mainly concentrate on two advanced multi-dimensional signal processing challenges for wireless systems that have attracted tremendous research attention in recent years, multi-carrier Multiple-Input Multiple-Output (MIMO) systems and multi-dimensional harmonic retrieval. As the key technologies of wireless communications, the numerous benefits of MIMO and multi-carrier modulation, e.g., boosting the data rate and improving the link reliability, have long been identified and have ignited great research interest. In particular, the Orthogonal Frequency Division Multiplexing (OFDM)-based multi-user MIMO downlink with Space-Division Multiple Access (SDMA) combines the twofold advantages of MIMO and multi-carrier modulation. It is the essential element ...

Cheng, Yao — Ilmenau University of Technology

Advanced Algebraic Concepts for Efficient Multi-Channel Signal Processing

Modern society is undergoing a fundamental change in the way we interact with technology. More and more devices are becoming "smart" by gaining advanced computation capabilities and communication interfaces, from household appliances over transportation systems to large-scale networks like the power grid. Recording, processing, and exchanging digital information is thus becoming increasingly important. As a growing share of devices is nowadays mobile and hence battery-powered, a particular interest in efficient digital signal processing techniques emerges. This thesis contributes to this goal by demonstrating methods for finding efficient algebraic solutions to various applications of multi-channel digital signal processing. These may not always result in the best possible system performance. However, they often come close while being significantly simpler to describe and to implement. The simpler description facilitates a thorough analysis of their performance which is crucial to design robust and reliable ...

Roemer, Florian — Ilmenau University of Technology

Generalized Consistent Estimation in Arbitrarily High Dimensional Signal Processing

The theory of statistical signal processing finds a wide variety of applications in the fields of data communications, such as in channel estimation, equalization and symbol detection, and sensor array processing, as in beamforming, and radar systems. Indeed, a large number of these applications can be interpreted in terms of a parametric estimation problem, typically approached by a linear filtering operation acting upon a set of multidimensional observations. Moreover, in many cases, the underlying structure of the observable signals is linear in the parameter to be inferred. This dissertation is devoted to the design and evaluation of statistical signal processing methods under realistic implementation conditions encountered in practice. Traditional statistical signal processing techniques intrinsically provide a good performance under the availability of a particularly high number of observations of fixed dimension. Indeed, the original optimality conditions cannot be theoretically guaranteed ...

Rubio, Francisco — Universitat Politecnica de Catalunya

Multi-microphone noise reduction and dereverberation techniques for speech applications

In typical speech communication applications, such as hands-free mobile telephony, voice-controlled systems and hearing aids, the recorded microphone signals are corrupted by background noise, room reverberation and far-end echo signals. This signal degradation can lead to total unintelligibility of the speech signal and decreases the performance of automatic speech recognition systems. In this thesis several multi-microphone noise reduction and dereverberation techniques are developed. In Part I we present a Generalised Singular Value Decomposition (GSVD) based optimal filtering technique for enhancing multi-microphone speech signals which are degraded by additive coloured noise. Several techniques are presented for reducing the computational complexity and we show that the GSVD-based optimal filtering technique can be integrated into a `Generalised Sidelobe Canceller' type structure. Simulations show that the GSVD-based optimal filtering technique achieves a larger signal-to-noise ratio improvement than standard fixed and adaptive beamforming techniques and ...

Doclo, Simon — Katholieke Universiteit Leuven

Direction Finding In The Presence of Array Imperfections, Model Mismatches and Multipath

In direction finding (DF) applications, there are several factors affecting the estimation accuracy of the direction-of-arrivals (DOA) of unknown source locations. The major distortions in the estimation process are due to the array imperfections, model mismatches and multipath. The array imperfections usually exist in practical applications due to the nonidealities in the antenna array such as mutual coupling (MC) and gain/phase uncertainties. The model mismatches usually occur when the model of the received signal differs from the signal model used in the processing stage of the DF system. Another distortion is due to multipath signals. In the multipath scenario, the antenna array receives the transmitted signal from more than one path with different directions and the array covariance matrix is rank-deficient. In this thesis, three new methods are proposed for the problems in DF applications in the presence of array ...

Elbir, Ahmet M. — Middle East Technical Univresity

Matrices, as natural representation of linear mappings in finite dimension, play a crucial role in signal processing and machine learning. Multiplying a vector by a full rank matrix a priori costs of the order of the number of non-zero entries in the matrix, in terms of arithmetic operations. However, matrices exist that can be applied much faster, this property being crucial to the success of certain linear transformations, such as the Fourier transform or the wavelet transform. What is the property that allows these matrices to be applied rapidly ? Is it easy to verify ? Can weapproximate matrices with ones having this property ? Can we estimate matrices having this property ? This thesis investigates these questions, exploring applications such as learning dictionaries with efficient implementations, accelerating the resolution of inverse problems or Fast Fourier Transform on graphs.

Le Magoarou, Luc — INRIA, Technicolor

Enhancement of Speech Signals - with a Focus on Voiced Speech Models

The topic of this thesis is speech enhancement with a focus on models of voiced speech. Speech is divided into two subcategories dependent on the characteristics of the signal. One part is the voiced speech, the other is the unvoiced. In this thesis, we primarily focus on the voiced speech parts and utilise the structure of the signal in relation to speech enhancement. The basis for the models is the harmonic model which is a very often used model for voiced speech because it describes periodic signals perfectly. First, we consider the problem of non-stationarity in the speech signal. The speech signal changes its characteristics continuously over time whereas most speech analysis and enhancement methods assume stationarity within 20-30 ms. We propose to change the model to allow the fundamental frequency to vary linearly over time by introducing a chirp ...

Nørholm, Sidsel Marie — Aalborg University

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