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

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Lifting transforms on graphs and their application to video coding

Compact representations of data are very useful in many applications such as coding, denoising or feature extraction. “Classical” transforms such as Discrete Cosine Transforms (DCT) or Discrete Wavelets Transforms (DWT) provide sparse approximations of smooth signals, but lose efficiency when they are applied to signals with large discontinuities. In such cases, directional transforms, which are able to adapt their basis functions to the underlying signal structure, improve the performance of “classical” transforms. In this PhD Thesis we describe a general class of lifting transforms on graphs that can be seen as N-dimensional directional transforms. Graphs are constructed so that every node corresponds to a specific sample point of a discrete N-dimensional signal and links between nodes represent correlation between samples. Therefore, non-correlated samples (e.g., samples across a large discontinuity in the signal) should not be linked. We propose a lifting-based directional transform that can be applied to any undirected graph. In this transform, filtering operations are performed following highcorrelation directions (indicated by the links between nodes), thus avoiding filtering across large discontinuities that give rise to large high-pass coefficients in those locations. In this way, the transform efficiently exploits the correlation that exists between data on the graph, leading to a more compact representation. We mainly focus on the design and optimization of these lifting transforms on graphs, studying and discussing the three main steps required to obtain an invertible and critically sampled transform: (i) graph construction, (ii) design of “good” graph bipartitions, and (iii) filter design. We also explain how to extend the transform to J levels of decomposition, obtaining a multiresolution analysis of the original N-dimensional signal. The proposed transform has many desirable properties, such as perfect reconstruction, critically-sampled, easy generalization to N-dimensional domains, non-separable and one-dimensional filtering operations, localization in frequency and in the original domain, and the ability to choose any filtering direction. As an application, we develop a graph-based video encoder where the goal is to obtain a compact representation of the original video sequence. To this end, we first propose a graph-representation of the video sequence and then design a 3-dimensional (spatio-temporal) non-separable directional transform. This can be viewed as an extension of wavelet transform-based video encoders that operate in the spatial and in the temporal domains independently. Our transform yields better compaction ability (in terms of non-linear approximation) than a state of the art motion-compensated temporal filtering transform (which can be interpreted as a temporal wavelet transform) and a comparable hybrid Discrete Cosine Transform (DCT)-based video encoder (which is the basis of the latest video coding standards). In order to obtain a complete video encoder, the transform coefficients and the side information (needed to obtain an invertible scheme) should be entropy coded and sent to the decoder. Therefore, we also propose a coefficient-reordering method based on the information of the graph which allows to improve the compression ability of the entropy encoder. Furthermore, we design two different low-cost approaches which aim to reduce the extensive computational complexity of the proposed system without causing significant losses of compression performance. The proposed complete system leads to an efficient encoder which significantly outperforms a comparable hybrid DCT-based encoder in rate-distortion terms. Finally, we investigate how rate-distortion optimization can be applied to the proposed coding scheme.La representación compacta de señales resulta útil en diversas aplicaciones, tales como compresión, reducción de ruido, o extracción de características. Transformadas “clásicas” como la Transformada Discreta del Coseno (DCT) o la TransformadaWavelet Discreta (DWT) logran aproximaciones compactas de señales suaves, pero pierden su eficiencia al ser aplicadas sobre se˜nales que contienen grandes discontinuidades. En estos casos, las transformadas direccionales, capaces de adaptar sus funciones base a la estructura de la señal a analizar, mejoran la eficiencia de las transformadas “clásicas”. En esta tesis nos centramos en el diseño y optimización de transformadas “lifting” sobre grafos, las cuales pueden ser interpretadas como transformadas direccionales N-dimensionales. Los grafos son construidos demanera que cada nodo se corresponde con una muestra específica de una señal discreta N-dimensional, y los enlaces entre los nodos representan correlación entre muestras. Así, muestras no correlacionadas (por ejemplo, muestras que se encuentran a ambos lados de una discontinuidad) no deberían estar unidas. Sobre el grafo formado aplicaremos transformadas basadas en el esquema “lifting”, en las que las operaciones de filtrado se realizan siguiendo las direcciones indicadas por los enlaces entre nodos (direcciones de alta correlación). De esta manera, evitaremos filtrar cruzando a través de largas discontinuidades (lo que resultaría en coeficientes con alto valor en dichas discontinuidades), dando lugar a una transformada direccional que explota la correlación que existe entre las muestras de la señal en el grafo, obteniendo una representación compacta de dicha señal. En esta tesis nos centramos, principalmente, en investigar los tres principales pasos requeridos para obtener una transformada direccional basada en el esquema “lifting” aplicado en grafos: (i) la construcción del grafo, (ii) el diseño de biparticiones del grafo, y (iii) la definición de los filtros. El buen diseño de estos tres procesos determinará, entre otras cosas, la capacidad para compactar la energía de la transformada. También explicamos cómo extender este tipo de transformadas a J niveles de descomposición, obteniendo un análisis multi-resolución de la señal N-dimensional original. La transformada propuesta tiene muchas propiedades deseables, tales como reconstrucción perfecta, muestreo crítico, fácil generalización a dominios N-dimensionales, operaciones de filtrado no separables y unidimensionales, localización en frecuencia y en el dominio original, y capacidad de elegir cualquier dirección de filtrado. Como aplicación, desarrollamos un codificador de vídeo basado en grafos donde el objetivo es obtener una versión compacta de la señal de vídeo original. Para ello, primero proponemos una representación en grafos de la secuencia de vídeo y luego diseñamos transformadas no separables direccionales 3-dimensionales (espacio-tiempo). Nuestro codificador puede interpretarse como una extensión de los codificadores de vídeo basados en “wavelets”, los cuales operan independientemente (de forma separable) en el dominio espacial y en el temporal. La transformada propuesta consigue mejores resultados (en términos de aproximación no lineal) que un método del estado del arte basado en “wavelets” temporales compensadas en movimiento, y un codificador DCT comparable (base de los últimos estándares de codificación de vídeo). Para conseguir un codificador de vídeo completo, los coeficientes resultantes de la transformada y la información secundaria (necesaria para obtener un esquema invertible) deben ser codificados entrópicamente y enviados al decodificador. Por ello, también proponemos en esta tesis un método de reordenación de los coeficientes basado en la información del grafo que permite mejorar la capacidad de compresión del codificador entrópico. El esquema de codificación propuesto mejora significativamente la eficiencia de un codificador híbrido basado en DCT en términos de tasa-distorsión. Sin embargo, nuestro método tiene la desventaja de su gran complejidad computacional. Para tratar de paliar este problema, diseñamos dos algoritmos que tratan de reducir dicha complejidad sin que ello afecte en la capacidad de compresión. Finalmente, investigamos como realizar optimización tasa-distorsión sobre el codificador basado en grafos propuesto

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Intelligent Circuits and Systems

ICICS-2020 is the third conference initiated by the School of Electronics and Electrical Engineering at Lovely Professional University that explored recent innovations of researchers working for the development of smart and green technologies in the fields of Energy, Electronics, Communications, Computers, and Control. ICICS provides innovators to identify new opportunities for the social and economic benefits of society.　 This conference bridges the gap between academics and R&D institutions, social visionaries, and experts from all strata of society to present their ongoing research activities and foster research relations between them. It provides opportunities for the exchange of new ideas, applications, and experiences in the field of smart technologies and finding global partners for future collaboration. The ICICS-2020 was conducted in two broad categories, Intelligent Circuits & Intelligent Systems and Emerging Technologies in Electrical Engineering

Intelligent Sensor Networks

In the last decade, wireless or wired sensor networks have attracted much attention. However, most designs target general sensor network issues including protocol stack (routing, MAC, etc.) and security issues. This book focuses on the close integration of sensing, networking, and smart signal processing via machine learning. Based on their world-class research, the authors present the fundamentals of intelligent sensor networks. They cover sensing and sampling, distributed signal processing, and intelligent signal learning. In addition, they present cutting-edge research results from leading experts

A Review of Resonant Converter Control Techniques and The Performances

paper first discusses each control technique and then gives experimental results and/or performance to highlights their merits. The resonant converter used as a case study is not specified to just single topology instead it used few topologies such as series-parallel resonant converter (SPRC), LCC resonant converter and parallel resonant converter (PRC). On the other hand, the control techniques presented in this paper are self-sustained phase shift modulation (SSPSM) control, self-oscillating power factor control, magnetic control and the H-∞ robust control technique

OBSERVER-BASED-CONTROLLER FOR INVERTED PENDULUM MODEL

This paper presents a state space control technique for inverted pendulum system. The system is a common classical control problem that has been widely used to test multiple control algorithms because of its nonlinear and unstable behavior. Full state feedback based on pole placement and optimal control is applied to the inverted pendulum system to achieve desired design specification which are 4 seconds settling time and 5% overshoot. The simulation and optimization of the full state feedback controller based on pole placement and optimal control techniques as well as the performance comparison between these techniques is described comprehensively. The comparison is made to choose the most suitable technique for the system that have the best trade-off between settling time and overshoot. Besides that, the observer design is analyzed to see the effect of pole location and noise present in the system

A Review of Resonant Converter Control Techniques and The Performances

paper first discusses each control technique and then gives experimental results and/or performance to highlights their merits. The resonant converter used as a case study is not specified to just single topology instead it used few topologies such as series-parallel resonant converter (SPRC), LCC resonant converter and parallel resonant converter (PRC). On the other hand, the control techniques presented in this paper are self-sustained phase shift modulation (SSPSM) control, self-oscillating power factor control, magnetic control and the H-∞ robust control technique

State-Feedback Controller Based on Pole Placement Technique for Inverted Pendulum System

This paper presents a state space control technique for inverted pendulum system using simulation and real experiment via MATLAB/SIMULINK software. The inverted pendulum is difficult system to control in the field of control engineering. It is also one of the most important classical control system problems because of its nonlinear characteristics and unstable system. It has three main problems that always appear in control application which are nonlinear system, unstable and non-minimumbehavior phase system. This project will apply state feedback controller based on pole placement technique which is capable in stabilizing the practical based inverted pendulum at vertical position. Desired design specifications which are 4 seconds settling time and 5 % overshoot is needed to apply in full state feedback controller based on pole placement technique. First of all, the mathematical model of an inverted pendulum system is derived to obtain the state space representation of the system. Then, the design phase of the State-Feedback Controller can be conducted after linearization technique is performed to the nonlinear equation with the aid of mathematical aided software such as Mathcad. After that, the design is simulated using MATLAB/Simulink software. The controller design of the inverted pendulum system is verified using simulation and experiment test. Finally the controller design is compared with PID controller for benchmarking purpose