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

PHM survey: implementation of signal processing methods for monitoring bearings and gearboxes

The reliability and safety of industrial equipments are one of the main objectives of companies to remain competitive in sectors that are more and more exigent in terms of cost and security. Thus, an unexpected shutdown can lead to physical injury as well as economic consequences. This paper aims to show the emergence of the Prognostics and Health Management (PHM) concept in the industry and to describe how it comes to complement the different maintenance strategies. It describes the benefits to be expected by the implementation of signal processing, diagnostic and prognostic methods in health-monitoring. More specifically, this paper provides a state of the art of existing signal processing techniques that can be used in the PHM strategy. This paper allows showing the diversity of possible techniques and choosing among them the one that will define a framework for industrials to monitor sensitive components like bearings and gearboxes

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

An Investigation of Orthogonal Wavelet Division Multiplexing Techniques as an Alternative to Orthogonal Frequency Division Multiplex Transmissions and Comparison of Wavelet Families and Their Children

Recently, issues surrounding wireless communications have risen to prominence because of the increase in the popularity of wireless applications. Bandwidth problems, and the difficulty of modulating signals across carriers, represent significant challenges. Every modulation scheme used to date has had limitations, and the use of the Discrete Fourier Transform in OFDM (Orthogonal Frequency Division Multiplex) is no exception. The restriction on further development of OFDM lies primarily within the type of transform it uses in the heart of its system, Fourier transform. OFDM suffers from sensitivity to Peak to Average Power Ratio, carrier frequency offset and wasting some bandwidth to guard successive OFDM symbols. The discovery of the wavelet transform has opened up a number of potential applications from image compression to watermarking and encryption. Very recently, work has been done to investigate the potential of using wavelet transforms within the communication space. This research will further investigate a recently proposed, innovative, modulation technique, Orthogonal Wavelet Division Multiplex, which utilises the wavelet transform opening a new avenue for an alternative modulation scheme with some interesting potential characteristics. Wavelet transform has many families and each of those families has children which each differ in filter length. This research consider comprehensively investigates the new modulation scheme, and proposes multi-level dynamic sub-banding as a tool to adapt variable signal bandwidths. Furthermore, all compactly supported wavelet families and their associated children of those families are investigated and evaluated against each other and compared with OFDM. The linear computational complexity of wavelet transform is less than the logarithmic complexity of Fourier in OFDM. The more important complexity is the operational complexity which is cost effectiveness, such as the time response of the system, the memory consumption and the number of iterative operations required for data processing. Those complexities are investigated for all available compactly supported wavelet families and their children and compared with OFDM. The evaluation reveals which wavelet families perform more effectively than OFDM, and for each wavelet family identifies which family children perform the best. Based on these results, it is concluded that the wavelet modulation scheme has some interesting advantages over OFDM, such as lower complexity and bandwidth conservation of up to 25%, due to the elimination of guard intervals and dynamic bandwidth allocation, which result in better cost effectiveness

Video transmission over wireless networks

Compressed video bitstream transmissions over wireless networks are addressed in this work. We first consider error control and power allocation for transmitting wireless video over CDMA networks in conjunction with multiuser detection. We map a layered video bitstream to several CDMA fading channels and inject multiple source/parity layers into each of these channels at the transmitter. We formulate a combined optimization problem and give the optimal joint rate and power allocation for each of linear minimum mean-square error (MMSE) multiuser detector in the uplink and two types of blind linear MMSE detectors, i.e., the direct-matrix-inversion (DMI) blind detector and the subspace blind detector, in the downlink. We then present a multiple-channel video transmission scheme in wireless CDMA networks over multipath fading channels. For a given budget on the available bandwidth and total transmit power, the transmitter determines the optimal power allocations and the optimal transmission rates among multiple CDMA channels, as well as the optimal product channel code rate allocation. We also make use of results on the large-system CDMA performance for various multiuser receivers in multipath fading channels. We employ a fast joint source-channel coding algorithm to obtain the optimal product channel code structure. Finally, we propose an end-to-end architecture for multi-layer progressive video delivery over space-time differentially coded orthogonal frequency division multiplexing (STDC-OFDM) systems. We propose to use progressive joint source-channel coding to generate operational transmission distortion-power-rate (TD-PR) surfaces. By extending the rate-distortion function in source coding to the TD-PR surface in joint source-channel coding, our work can use the ??equal slope?? argument to effectively solve the transmission rate allocation problem as well as the transmission power allocation problem for multi-layer video transmission. It is demonstrated through simulations that as the wireless channel conditions change, these proposed schemes can scale the video streams and transport the scaled video streams to receivers with a smooth change of perceptual quality

3D multiple description coding for error resilience over wireless networks

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Mobile communications has gained a growing interest from both customers and service providers alike in the last 1-2 decades. Visual information is used in many application domains such as remote health care, video –on demand, broadcasting, video surveillance etc. In order to enhance the visual effects of digital video content, the depth perception needs to be provided with the actual visual content. 3D video has earned a significant interest from the research community in recent years, due to the tremendous impact it leaves on viewers and its enhancement of the user’s quality of experience (QoE). In the near future, 3D video is likely to be used in most video applications, as it offers a greater sense of immersion and perceptual experience. When 3D video is compressed and transmitted over error prone channels, the associated packet loss leads to visual quality degradation. When a picture is lost or corrupted so severely that the concealment result is not acceptable, the receiver typically pauses video playback and waits for the next INTRA picture to resume decoding. Error propagation caused by employing predictive coding may degrade the video quality severely. There are several ways used to mitigate the effects of such transmission errors. One widely used technique in International Video Coding Standards is error resilience. The motivation behind this research work is that, existing schemes for 2D colour video compression such as MPEG, JPEG and H.263 cannot be applied to 3D video content. 3D video signals contain depth as well as colour information and are bandwidth demanding, as they require the transmission of multiple high-bandwidth 3D video streams. On the other hand, the capacity of wireless channels is limited and wireless links are prone to various types of errors caused by noise, interference, fading, handoff, error burst and network congestion. Given the maximum bit rate budget to represent the 3D scene, optimal bit-rate allocation between texture and depth information rendering distortion/losses should be minimised. To mitigate the effect of these errors on the perceptual 3D video quality, error resilience video coding needs to be investigated further to offer better quality of experience (QoE) to end users. This research work aims at enhancing the error resilience capability of compressed 3D video, when transmitted over mobile channels, using Multiple Description Coding (MDC) in order to improve better user’s quality of experience (QoE). Furthermore, this thesis examines the sensitivity of the human visual system (HVS) when employed to view 3D video scenes. The approach used in this study is to use subjective testing in order to rate people’s perception of 3D video under error free and error prone conditions through the use of a carefully designed bespoke questionnaire.Petroleum Technology Development Fund (PTDF

Gear dynamics monitoring using discrete wavelet transformation and multi-layer perceptron neural networks

This paper presents a multi-stage algorithm for the dynamic condition monitoring of a gear. The algorithm provides information referred to the gear status (fault or normal condition) and estimates the mesh stiffness per shaft revolution in case that any abnormality is detected. In the first stage, the analysis of coefficients generated through discrete wavelet transformation (DWT) is proposed as a fault detection and localization tool. The second stage consists in establishing the mesh stiffness reduction associated with local failures by applying a supervised learning mode and coupled with analytical models. To do this, a multi-layer perceptron neural network has been configured using as input features statistical parameters sensitive to torsional stiffness decrease and derived from wavelet transforms of the response signal. The proposed method is applied to the gear condition monitoring and results show that it can update the mesh dynamic properties of the gear on line