Generic Invertibility of Multidimensional FIR Filter Banks and MIMO Systems

We study the invertibility of M-variate Laurent polynomial N × P matrices. Such matrices represent multidimensional systems in various settings such as filter banks, multiple-input multiple-output systems, and multirate systems. Given an N × P Laurent polynomial matrix H(z1,..., zM) of degree at most k, we want to find a P × N Laurent polynomial left inverse matrix G(z) of H(z) such that G(z)H(z) = I. We provide computable conditions to test the invertibility and propose algorithms to find a particular inverse. The main result of this paper is to prove that H(z) is generically invertible when N −P ≥ M; whereas when N −P < M, then H(z) is generically noninvertible. As a result, we propose an algorithm to find a particular inverse of a Laurent polynomial matrix that is faster than current algorithms known to us

Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems

We study the feasibility of short finite impulse response (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with oversampling factors of at least two, we provide prescriptions for the shortest filter length of the synthesis bank that would guarantee PR almost surely. The prescribed length is as short or shorter than the analysis filters and has an approximate inverse relationship with the oversampling factor. Our results are in form of necessary and sufficient statements that hold generically, hence only fail for elaborately-designed nongeneric examples. We provide extensive numerical verification of the theoretical results and demonstrate that the gap between the derived filter length prescriptions and the true minimum is small. The results have potential applications in synthesis FB design problems, where the analysis bank is given, and for analysis of fundamental limitations in blind signals reconstruction from data collected by unknown subsampled multi-channel systems.Comment: Manuscript submitted to IEEE Transactions on Signal Processin

Adaptive Algorithms for Intelligent Acoustic Interfaces

Modern speech communications are evolving towards a new direction which involves users in a more perceptive way. That is the immersive experience, which may be considered as the “last-mile” problem of telecommunications. One of the main feature of immersive communications is the distant-talking, i.e. the hands-free (in the broad sense) speech communications without bodyworn or tethered microphones that takes place in a multisource environment where interfering signals may degrade the communication quality and the intelligibility of the desired speech source. In order to preserve speech quality intelligent acoustic interfaces may be used. An intelligent acoustic interface may comprise multiple microphones and loudspeakers and its peculiarity is to model the acoustic channel in order to adapt to user requirements and to environment conditions. This is the reason why intelligent acoustic interfaces are based on adaptive filtering algorithms. The acoustic path modelling entails a set of problems which have to be taken into account in designing an adaptive filtering algorithm. Such problems may be basically generated by a linear or a nonlinear process and can be tackled respectively by linear or nonlinear adaptive algorithms. In this work we consider such modelling problems and we propose novel effective adaptive algorithms that allow acoustic interfaces to be robust against any interfering signals, thus preserving the perceived quality of desired speech signals. As regards linear adaptive algorithms, a class of adaptive filters based on the sparse nature of the acoustic impulse response has been recently proposed. We adopt such class of adaptive filters, named proportionate adaptive filters, and derive a general framework from which it is possible to derive any linear adaptive algorithm. Using such framework we also propose some efficient proportionate adaptive algorithms, expressly designed to tackle problems of a linear nature. On the other side, in order to address problems deriving from a nonlinear process, we propose a novel filtering model which performs a nonlinear transformations by means of functional links. Using such nonlinear model, we propose functional link adaptive filters which provide an efficient solution to the modelling of a nonlinear acoustic channel. Finally, we introduce robust filtering architectures based on adaptive combinations of filters that allow acoustic interfaces to more effectively adapt to environment conditions, thus providing a powerful mean to immersive speech communications

Adaptive Algorithms for Intelligent Acoustic Interfaces

Modern speech communications are evolving towards a new direction which involves users in a more perceptive way. That is the immersive experience, which may be considered as the “last-mile” problem of telecommunications. One of the main feature of immersive communications is the distant-talking, i.e. the hands-free (in the broad sense) speech communications without bodyworn or tethered microphones that takes place in a multisource environment where interfering signals may degrade the communication quality and the intelligibility of the desired speech source. In order to preserve speech quality intelligent acoustic interfaces may be used. An intelligent acoustic interface may comprise multiple microphones and loudspeakers and its peculiarity is to model the acoustic channel in order to adapt to user requirements and to environment conditions. This is the reason why intelligent acoustic interfaces are based on adaptive filtering algorithms. The acoustic path modelling entails a set of problems which have to be taken into account in designing an adaptive filtering algorithm. Such problems may be basically generated by a linear or a nonlinear process and can be tackled respectively by linear or nonlinear adaptive algorithms. In this work we consider such modelling problems and we propose novel effective adaptive algorithms that allow acoustic interfaces to be robust against any interfering signals, thus preserving the perceived quality of desired speech signals. As regards linear adaptive algorithms, a class of adaptive filters based on the sparse nature of the acoustic impulse response has been recently proposed. We adopt such class of adaptive filters, named proportionate adaptive filters, and derive a general framework from which it is possible to derive any linear adaptive algorithm. Using such framework we also propose some efficient proportionate adaptive algorithms, expressly designed to tackle problems of a linear nature. On the other side, in order to address problems deriving from a nonlinear process, we propose a novel filtering model which performs a nonlinear transformations by means of functional links. Using such nonlinear model, we propose functional link adaptive filters which provide an efficient solution to the modelling of a nonlinear acoustic channel. Finally, we introduce robust filtering architectures based on adaptive combinations of filters that allow acoustic interfaces to more effectively adapt to environment conditions, thus providing a powerful mean to immersive speech communications

Introduction to frames

This survey gives an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox and have become popular through use in numerous applications. Our aim is to familiarize a general audience with the area, while at the same time giving a snapshot of the current state-of-the-art

Efficient FPGA implementation and power modelling of image and signal processing IP cores

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Field Programmable Gate Arrays (FPGAs) are the technology of choice in a number ofimage and signal processing application areas such as consumer electronics, instrumentation, medical data processing and avionics due to their reasonable energy consumption, high performance, security, low design-turnaround time and reconfigurability. Low power FPGA devices are also emerging as competitive solutions for mobile and thermally constrained platforms. Most computationally intensive image and signal processing algorithms also consume a lot of power leading to a number of issues including reduced mobility, reliability concerns and increased design cost among others. Power dissipation has become one of the most important challenges, particularly for FPGAs. Addressing this problem requires optimisation and awareness at all levels in the design flow. The key achievements of the work presented in this thesis are summarised here. Behavioural level optimisation strategies have been used for implementing matrix product and inner product through the use of mathematical techniques such as Distributed Arithmetic (DA) and its variations including offset binary coding, sparse factorisation and novel vector level transformations. Applications to test the impact of these algorithmic and arithmetic transformations include the fast Hadamard/Walsh transforms and Gaussian mixture models. Complete design space exploration has been performed on these cores, and where appropriate, they have been shown to clearly outperform comparable existing implementations. At the architectural level, strategies such as parallelism, pipelining and systolisation have been successfully applied for the design and optimisation of a number of cores including colour space conversion, finite Radon transform, finite ridgelet transform and circular convolution. A pioneering study into the influence of supply voltage scaling for FPGA based designs, used in conjunction with performance enhancing strategies such as parallelism and pipelining has been performed. Initial results are very promising and indicated significant potential for future research in this area. A key contribution of this work includes the development of a novel high level power macromodelling technique for design space exploration and characterisation of custom IP cores for FPGAs, called Functional Level Power Analysis and Modelling (FLPAM). FLPAM is scalable, platform independent and compares favourably with existing approaches. A hybrid, top-down design flow paradigm integrating FLPAM with commercially available design tools for systematic optimisation of IP cores has also been developed

Efficient FPGA implementation and power modelling of image and signal processing IP cores

Field Programmable Gate Arrays (FPGAs) are the technology of choice in a number ofimage and signal processing application areas such as consumer electronics, instrumentation, medical data processing and avionics due to their reasonable energy consumption, high performance, security, low design-turnaround time and reconfigurability. Low power FPGA devices are also emerging as competitive solutions for mobile and thermally constrained platforms. Most computationally intensive image and signal processing algorithms also consume a lot of power leading to a number of issues including reduced mobility, reliability concerns and increased design cost among others. Power dissipation has become one of the most important challenges, particularly for FPGAs. Addressing this problem requires optimisation and awareness at all levels in the design flow. The key achievements of the work presented in this thesis are summarised here. Behavioural level optimisation strategies have been used for implementing matrix product and inner product through the use of mathematical techniques such as Distributed Arithmetic (DA) and its variations including offset binary coding, sparse factorisation and novel vector level transformations. Applications to test the impact of these algorithmic and arithmetic transformations include the fast Hadamard/Walsh transforms and Gaussian mixture models. Complete design space exploration has been performed on these cores, and where appropriate, they have been shown to clearly outperform comparable existing implementations. At the architectural level, strategies such as parallelism, pipelining and systolisation have been successfully applied for the design and optimisation of a number of cores including colour space conversion, finite Radon transform, finite ridgelet transform and circular convolution. A pioneering study into the influence of supply voltage scaling for FPGA based designs, used in conjunction with performance enhancing strategies such as parallelism and pipelining has been performed. Initial results are very promising and indicated significant potential for future research in this area. A key contribution of this work includes the development of a novel high level power macromodelling technique for design space exploration and characterisation of custom IP cores for FPGAs, called Functional Level Power Analysis and Modelling (FLPAM). FLPAM is scalable, platform independent and compares favourably with existing approaches. A hybrid, top-down design flow paradigm integrating FLPAM with commercially available design tools for systematic optimisation of IP cores has also been developed.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior