On the design and implementation of a class of multiplier-less two-channel 1-D and 2-D nonseparable PR FIR filterbanks

This paper proposes a new design and implementation method for a class of multiplierless 2-channel 1D and 2D nonseparable perfect reconstruction (PR) filterbanks (FB). It is based on the structure proposed by S.M. Phoong et al. (see IEEE Trans. Sig. Proc., vol.43, p.649-64, 1995) and the use of multiplier blocks (MB). The latter technique allows one to further reduce the number of adders in implementing these multiplier-less FB by almost 50%, compared to the conventional method using sum of powers of two coefficients (SOPOT) alone. Furthermore, by generalizing the 1D to 2D transformation of Phoong et al., new 2D PR FBs with quincunx, hourglass, and parallelogram spectral support are obtained. These nonseparable FBs can be cascaded to realize new multiplierless PR directional FB for image processing and motion analysis. Design examples are given to demonstrate the usefulness of the proposed method.published_or_final_versio

Design and Implementation of Complexity Reduced Digital Signal Processors for Low Power Biomedical Applications

Wearable health monitoring systems can provide remote care with supervised, inde-pendent living which are capable of signal sensing, acquisition, local processing and transmission. A generic biopotential signal (such as Electrocardiogram (ECG), and Electroencephalogram (EEG)) processing platform consists of four main functional components. The signals acquired by the electrodes are amplified and preconditioned by the (1) Analog-Front-End (AFE) which are then digitized via the (2) Analog-to-Digital Converter (ADC) for further processing. The local digital signal processing is usually handled by a custom designed (3) Digital Signal Processor (DSP) which is responsible for either anyone or combination of signal processing algorithms such as noise detection, noise/artefact removal, feature extraction, classification and compres-sion. The digitally processed data is then transmitted via the (4) transmitter which is renown as the most power hungry block in the complete platform. All the afore-mentioned components of the wearable systems are required to be designed and fitted into an integrated system where the area and the power requirements are stringent. Therefore, hardware complexity and power dissipation of each functional component are crucial aspects while designing and implementing a wearable monitoring platform. The work undertaken focuses on reducing the hardware complexity of a biosignal DSP and presents low hardware complexity solutions that can be employed in the aforemen-tioned wearable platforms. A typical state-of-the-art system utilizes Sigma Delta (Σ∆) ADCs incorporating a Σ∆ modulator and a decimation filter whereas the state-of-the-art decimation filters employ linear phase Finite-Impulse-Response (FIR) filters with high orders that in-crease the hardware complexity [1–5]. In this thesis, the novel use of minimum phase Infinite-Impulse-Response (IIR) decimators is proposed where the hardware complexity is massively reduced compared to the conventional FIR decimators. In addition, the non-linear phase effects of these filters are also investigated since phase non-linearity may distort the time domain representation of the signal being filtered which is un-desirable effect for biopotential signals especially when the fiducial characteristics carry diagnostic importance. In the case of ECG monitoring systems the effect of the IIR filter phase non-linearity is minimal which does not affect the diagnostic accuracy of the signals. The work undertaken also proposes two methods for reducing the hardware complexity of the popular biosignal processing tool, Discrete Wavelet Transform (DWT). General purpose multipliers are known to be hardware and power hungry in terms of the number of addition operations or their underlying building blocks like full adders or half adders required. Higher number of adders leads to an increase in the power consumption which is directly proportional to the clock frequency, supply voltage, switching activity and the resources utilized. A typical Field-Programmable-Gate-Array’s (FPGA) resources are Look-up Tables (LUTs) whereas a custom Digital Signal Processor’s (DSP) are gate-level cells of standard cell libraries that are used to build adders [6]. One of the proposed methods is the replacement of the hardware and power hungry general pur-pose multipliers and the coefficient memories with reconfigurable multiplier blocks that are composed of simple shift-add networks and multiplexers. This method substantially reduces the resource utilization as well as the power consumption of the system. The second proposed method is the design and implementation of the DWT filter banks using IIR filters which employ less number of arithmetic operations compared to the state-of-the-art FIR wavelets. This reduces the hardware complexity of the analysis filter bank of the DWT and can be employed in applications where the reconstruction is not required. However, the synthesis filter bank for the IIR wavelet transform has a higher computational complexity compared to the conventional FIR wavelet synthesis filter banks since re-indexing of the filtered data sequence is required that can only be achieved via the use of extra registers. Therefore, this led to the proposal of a novel design which replaces the complex IIR based synthesis filter banks with FIR fil-ters which are the approximations of the associated IIR filters. Finally, a comparative study is presented where the hybrid IIR/FIR and FIR/FIR wavelet filter banks are de-ployed in a typical noise reduction scenario using the wavelet thresholding techniques. It is concluded that the proposed hybrid IIR/FIR wavelet filter banks provide better denoising performance, reduced computational complexity and power consumption in comparison to their IIR/IIR and FIR/FIR counterparts

Biorthogonal partners and applications

Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Role of anticausal inverses in multirate filter-banks. II. The FIR case, factorizations, and biorthogonal lapped transforms

For pt. I see ibid., vol.43, no.5, p.1090, 1990. In part I we studied the system-theoretic properties of discrete time transfer matrices in the context of inversion, and classified them according to the types of inverses they had. In particular, we outlined the role of causal FIR matrices with anticausal FIR inverses (abbreviated cafacafi) in the characterization of FIR perfect reconstruction (PR) filter banks. Essentially all FIR PR filter banks can be characterized by causal FIR polyphase matrices having anticausal FIR inverses. In this paper, we introduce the most general degree-one cafacafi building block, and consider the problem of factorizing cafacafi systems into these building blocks. Factorizability conditions are developed. A special class of cafacafi systems called the biorthogonal lapped transform (BOLT) is developed, and shown to be factorizable. This is a generalization of the well-known lapped orthogonal transform (LOT). Examples of unfactorizable cafacafi systems are also demonstrated. Finally it is shown that any causal FIR matrix with FIR inverse can be written as a product of a factorizable cafacafi system and a unimodular matrix

Principles, fundamentals, and applications of programmable integrated photonics

[EN] Programmable integrated photonics is an emerging new paradigm that aims at designing common integrated optical hardware resource configurations, capable of implementing an unconstrained variety of functionalities by suitable programming, following a parallel but not identical path to that of integrated electronics in the past two decades of the last century. Programmable integrated photonics is raising considerable interest, as it is driven by the surge of a considerable number of new applications in the fields of telecommunications, quantum information processing, sensing, and neurophotonics, calling for flexible, reconfigurable, low-cost, compact, and low-power-consuming devices that can cooperate with integrated electronic devices to overcome the limitation expected by the demise of Moore¿s Law. Integrated photonic devices exploiting full programmability are expected to scale from application-specific photonic chips (featuring a relatively low number of functionalities) up to very complex application-agnostic complex subsystems much in the same way as field programmable gate arrays and microprocessors operate in electronics. Two main differences need to be considered. First, as opposed to integrated electronics, programmable integrated photonics will carry analog operations over the signals to be processed. Second, the scale of integration density will be several orders of magnitude smaller due to the physical limitations imposed by the wavelength ratio of electrons and light wave photons. The success of programmable integrated photonics will depend on leveraging the properties of integrated photonic devices and, in particular, on research into suitable interconnection hardware architectures that can offer a very high spatial regularity as well as the possibility of independently setting (with a very low power consumption) the interconnection state of each connecting element. Integrated multiport interferometers and waveguide meshes provide regular and periodic geometries, formed by replicating unit elements and cells, respectively. In the case of waveguide meshes, the cells can take the form of a square, hexagon, or triangle, among other configurations. Each side of the cell is formed by two integrated waveguides connected by means of a Mach¿Zehnder interferometer or a tunable directional coupler that can be operated by means of an output control signal as a crossbar switch or as a variable coupler with independent power division ratio and phase shift. In this paper, we provide the basic foundations and principles behind the construction of these complex programmable circuits. We also review some practical aspects that limit the programming and scalability of programmable integrated photonics and provide an overview of some of the most salient applications demonstrated so far.European Research Council; Conselleria d'Educació, Investigació, Cultura i Esport; Ministerio de Ciencia, Innovación y Universidades; European Cooperation in Science and Technology; Horizon 2020 Framework Programme.Pérez-López, D.; Gasulla Mestre, I.; Dasmahapatra, P.; Capmany Francoy, J. (2020). Principles, fundamentals, and applications of programmable integrated photonics. Advances in Optics and Photonics. 12(3):709-786. https://doi.org/10.1364/AOP.387155709786123Lyke, J. C., Christodoulou, C. G., Vera, G. A., & Edwards, A. H. (2015). An Introduction to Reconfigurable Systems. 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Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

NATURAL ALGORITHMS IN DIGITAL FILTER DESIGN

Digital filters are an important part of Digital Signal Processing (DSP), which plays vital roles within the modern world, but their design is a complex task requiring a great deal of specialised knowledge. An analysis of this design process is presented, which identifies opportunities for the application of optimisation. The Genetic Algorithm (GA) and Simulated Annealing are problem-independent and increasingly popular optimisation techniques. They do not require detailed prior knowledge of the nature of a problem, and are unaffected by a discontinuous search space, unlike traditional methods such as calculus and hill-climbing. Potential applications of these techniques to the filter design process are discussed, and presented with practical results. Investigations into the design of Frequency Sampling (FS) Finite Impulse Response (FIR) filters using a hybrid GA/hill-climber proved especially successful, improving on published results. An analysis of the search space for FS filters provided useful information on the performance of the optimisation technique. The ability of the GA to trade off a filter's performance with respect to several design criteria simultaneously, without intervention by the designer, is also investigated. Methods of simplifying the design process by using this technique are presented, together with an analysis of the difficulty of the non-linear FIR filter design problem from a GA perspective. This gave an insight into the fundamental nature of the optimisation problem, and also suggested future improvements. The results gained from these investigations allowed the framework for a potential 'intelligent' filter design system to be proposed, in which embedded expert knowledge, Artificial Intelligence techniques and traditional design methods work together. This could deliver a single tool capable of designing a wide range of filters with minimal human intervention, and of proposing solutions to incomplete problems. It could also provide the basis for the development of tools for other areas of DSP system design