Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

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

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

Development of Multirate Filter – Based Region Features for Iris Identification

The emergence of biometric system is seen as the next-generation technological solution in strengthening the social and national security. The evolution of biometrics has shifted the paradigm of authentication from classical token and knowledge-based systems to physiological and behavioral trait based systems. R & D on iris biometrics, in last one decade, has established it as one of the most promising traits. Even though, iris biometric takes high resolution near-infrared (NIR) images as input, its authentication accuracy is very commendable. Its performance is often influenced by the presence of noise, database size, and feature representation. This thesis focuses on the use of multi resolution analysis (MRA) in developing suitable features for non-ideal iris images. Our investigation starts with the iris feature extraction technique using Cohen −Daubechies − Feauveau 9/7 (CDF 9/7) filter bank. In this work, a technique has been proposed to deal with issues like segmentation failure and occlusion. The experimental studies deal with the superiority of CDF 9/7 filter bank over the frequency based techniques. Since there is scope for improving the frequency selectivity of CDF 9/7 filter bank, a tunable filter bank is proposed to extract region based features from non-cooperative iris images. The proposed method is based on half band polynomial of 14th order. Since, regularity and frequency selectivity are in inverse relationship with each other, filter coefficients are derived by not imposing maximum number of zeros. Also, the half band polynomial is presented in x-domain, so as to apply semidefinite programming, which results in optimization of coefficients of analysis/synthesis filter. The next contribution in this thesis deals with the development of another powerful MRA known as triplet half band filter bank (THFB). The advantage of THFB is the flexibility in choosing the frequency response that allows one to overcome the magnitude constraints. The proposed filter bank has improved frequency selectivity along with other desired properties, which is then used for iris feature extraction. The last contribution of the thesis describes a wavelet cepstral feature derived from CDF 9/7 filter bank to characterize iris texture. Wavelet cepstrum feature helps in reducing the dimensionality of the detail coefficients; hence, a compact feature presentation is possible with improved accuracy against CDF 9/7. The efficacy of the features suggested are validated for iris recognition on three publicly available databases namely, CASIAv3, UBIRISv1, and IITD. The features are compared with other transform domain features like FFT, Gabor filter and a comprehensive evaluation is done for all suggested features as well. It has been observed that the suggested features show superior performance with respect to accuracy. Among all suggested features, THFB has shown best performance

Scalable and perceptual audio compression

This thesis deals with scalable perceptual audio compression. Two scalable perceptual solutions as well as a scalable to lossless solution are proposed and investigated. One of the scalable perceptual solutions is built around sinusoidal modelling of the audio signal whilst the other is built on a transform coding paradigm. The scalable coders are shown to scale both in a waveform matching manner as well as a psychoacoustic manner. In order to measure the psychoacoustic scalability of the systems investigated in this thesis, the similarity between the original signal\u27s psychoacoustic parameters and that of the synthesized signal are compared. The psychoacoustic parameters used are loudness, sharpness, tonahty and roughness. This analysis technique is a novel method used in this thesis and it allows an insight into the perceptual distortion that has been introduced by any coder analyzed in this manner

Diagnostic des machines dans le plan temps-fréquence

Using short-time Fourier transform in machinery fault diagnosis -- Time-frequency distributions and their application to machinery fault detection -- Application of wavelet transform in machine fault detection -- Time-frequency algorithms and their applications

Multidimensional Wavelets and Computer Vision

This report deals with the construction and the mathematical analysis of multidimensional nonseparable wavelets and their efficient application in computer vision. In the first part, the fundamental principles and ideas of multidimensional wavelet filter design such as the question for the existence of good scaling matrices and sensible design criteria are presented and extended in various directions. Afterwards, the analytical properties of these wavelets are investigated in some detail. It will turn out that they are especially well-suited to represent (discretized) data as well as large classes of operators in a sparse form - a property that directly yields efficient numerical algorithms. The final part of this work is dedicated to the application of the developed methods to the typical computer vision problems of nonlinear image regularization and the computation of optical flow in image sequences. It is demonstrated how the wavelet framework leads to stable and reliable results for these problems of generally ill-posed nature. Furthermore, all the algorithms are of order O(n) leading to fast processing

Development of new fault detection methods for rotating machines (roller bearings)

Abstract Early fault diagnosis of roller bearings is extremely important for rotating machines, especially for high speed, automatic and precise machines. Many research efforts have been focused on fault diagnosis and detection of roller bearings, since they constitute one the most important elements of rotating machinery. In this study a combination method is proposed for early damage detection of roller bearing. Wavelet packet transform (WPT) is applied to the collected data for denoising and the resulting clean data are break-down into some elementary components called Intrinsic mode functions (IMFs) using Ensemble empirical mode decomposition (EEMD) method. The normalized energy of three first IMFs are used as input for Support vector machine (SVM) to recognize whether signals are sorting out from healthy or faulty bearings. Then, since there is no robust guide to determine amplitude of added noise in EEMD technique, a new Performance improved EEMD (PIEEMD) is proposed to determine the appropriate value of added noise. A novel feature extraction method is also proposed for detecting small size defect using Teager-Kaiser energy operator (TKEO). TKEO is applied to IMFs obtained to create new feature vectors as input data for one-class SVM. The results of applying the method to acceleration signals collected from an experimental bearing test rig demonstrated that the method can be successfully used for early damage detection of roller bearings. Most of the diagnostic methods that have been developed up to now can be applied for the case stationary working conditions only (constant speed and load). However, bearings often work at time-varying conditions such as wind turbine supporting bearings, mining excavator bearings, vehicles, robots and all processes with run-up and run-down transients. Damage identification for bearings working under non-stationary operating conditions, especially for early/small defects, requires the use of appropriate techniques, which are generally different from those used for the case of stationary conditions, in order to extract fault-sensitive features which are at the same time insensitive to operational condition variations. Some methods have been proposed for damage detection of bearings working under time-varying speed conditions. However, their application might increase the instrumentation cost because of providing a phase reference signal. Furthermore, some methods such as order tracking methods still can be applied when the speed variation is limited. In this study, a novel combined method based on cointegration is proposed for the development of fault features which are sensitive to the presence of defects while in the same time they are insensitive to changes in the operational conditions. It does not require any additional measurements and can identify defects even for considerable speed variations. The signals acquired during run-up condition are decomposed into IMFs using the performance improved EEMD method. Then, the cointegration method is applied to the intrinsic mode functions to extract stationary residuals. The feature vectors are created by applying the Teager-Kaiser energy operator to the obtained stationary residuals. Finally, the feature vectors of the healthy bearing signals are utilized to construct a separating hyperplane using one-class support vector machine. Eventually the proposed method was applied to vibration signals measured on an experimental bearing test rig. The results verified that the method can successfully distinguish between healthy and faulty bearings even if the shaft speed changes dramatically