Spectral Analysis of Seismic Data Using Wavelet Transform

Spectral analysis provides the frequency information of the data. Fourier tansform projects the data from time domain into frequency domain, while the time information is completely lost after the procedure. Time-frequency analysis is a procedure to localiza the frequency content in time. Wavelet transform is a method to do the time-frequency analysis of the data. Many methods of wavelet transform have been developed such as the continuous wavelet transform, the multiresolution analysis, the wavelet packet and the matching pursuit decomposition. Each method has its own advantages of providing a time-frequency representation of the data. In the thesis, different methods of wavelet transform are introduced and performed on different data. The advantages and the disadvantages of different methods are analyzed so that different methods of wavelet transform could be applied in different situations. In practice, different methods should be used together to provide an good time-frequency representation for different data

Multiple Change-point Detection for piecewise stationary categorical time series

In this dissertation, we propose a fast yet consistent method for segmenting a piecewise stationary categorical-valued time series, with a finite unknown number of change-points in its autocovariance structure. To avoid loss of information, instead of arbitrarily assigning numerical numbers in analysis of the original time series, we focus on the multinomial process, which is derived by denoting each category of the original series as a unit vector. The corresponding multinomial process is then modeled by a nonparametric multivariate locally stationary wavelet process, where the piecewise constant autocovariance structure for any given variate is completely described by the wavelet periodograms for that variate at multiple scales and locations. Further, we propose a criterion that optimally selects the scalings and provides the generation of the trace statistics whose mean functions inherit the piecewise constancy. The resulting statistics will serve as input sequences for later segmentation. Change-point detection is accomplished by first examining the input sequence at each scale with the binary segmentation procedure, and then combining the detected breakpoints across scales. The consistency result of our method is established under certain conditions. In addition, several simulation studies and a real-data analysis of a DNA sequence are provided to demonstrate the viability of our methodology

Adapted wavelet analysis from theory to software

This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data. It contains an overview of mathematical prerequisites and proceeds to describe hands-on programming techniques to implement special programs for signal analysis and other applications. From the table of contents: - Mathematical Preliminaries - Programming Techniques - The Discrete Fourier Transform - Local Trigonometric Transforms - Quadrature Filters - The Discrete Wavelet Transform - Wavelet Packets - The Best Basis Algorithm - Multidimensional Library Trees - Time-Frequency Analysis - Some Applications - Solutions to Some of the Exercises - List of Symbols - Quadrature Filter Coefficient

The design, implementation and analysis of a wavelet-based video codec

Includes bibliographical references.The Wavelet Transform has been shown to be highly effective in image coding applications. This thesis describes the development of a new wavelet-based video compression algorithm which is based on the 3D wavelet transform, and requires no complicated motion estimation techniques. The proposed codec processes a sequence of images in a group of frames (GOF) by first transforming the group spatially and temporally, in order to obtain a GOF of 3D approximation and detail coefficients. The codec uses selective prediction of temporal approximation coefficients in order to decorrelate transformed GOFs. Following this, a modified version of Said and Pearlman's image coding technique of Set Partitioning in Hierarchical Trees is used as a method for encoding the transformed GOF. The compression algorithm has been implemented in software, and tested on seven test sequences at different bit-rates. Experimental results indicate a significantly improved performance over MPEG 1 and 2 in terms of picture quality, for sequences filmed with a stationary camera. The codec also performs well on scenes filmed with a moving camera, provided that there is not a large degree of spatial detail present. In addition, the proposed codec has several attractive features. It performs well without entropy coding, and does not require any computationally-expensive motion estimation methods, such as those used by MPEG. Finally, a substantial advantage is that the encoder generates a bit-stream which allows for the progressive transmission of video, making it well-suited to use in video applications over digital networks

A Low Power Application-Specific Integrated Circuit (ASIC) Implementation of Wavelet Transform/Inverse Transform

A unique ASIC was designed implementing the Haar Wavelet transform for image compression/decompression. ASIC operations include performing the Haar wavelet transform on a 512 by 512 square pixel image, preparing the image for transmission by quantizing and thresholding the transformed data, and performing the inverse Haar wavelet transform, returning the original image with only minor degradation. The ASIC is based on an existing four-chip FPGA implementation. Implementing the design using a dedicated ASIC enhances the speed, decreases chip count to a single die, and uses significantly less power compared to the FPGA implementation. A reduction of RAM accesses was realized and a tradeoff between states and duplication of components for parallel operation were key to the performance gains. Almost half of the external RAM accesses were removed from the FPGA design by incorporating an internal register file. This reduction reduced the number of states needed to process an image increasing the image frame rate by 13% and decreased I/O traffic on the bus by 47%. Adding control lines to the ALU components, thus eliminating unnecessary switching of combination logic blocks, further reduced power requirements. The 22 mm2 ASIC consumes an estimated 430 mW of power when operating at the maximum frequency of 17 MHz

Implementación en DSPs de técnicas de comunicación basadas en Wavelets

Se presentan los resultados del proyecto de investigación “Implementación en DSPs de Técnicas de Comunicación basadas en Wavelets”, cuyo propósito es la construcción de sistemas en tiempo real que hacen uso de tecnología DSP (Procesador Digital de Señales) para aplicaciones en sistemas de comunicaciones. Para el diseño de los algoritmos se hace uso de técnicas derivadas del tratamiento wavelet. Para tal efecto se propone: un esquema de compresión híbrido basado en los paquetes wavelet y los coeficientes de predicción LPC; un sistema de sincronización para la técnica de multiplexación por división de paquetes wavelet (WPDM); y un sistema de encriptación híbrido basado en wavelets y sistemas caóticos. Se presentan diferentes pruebas de desempeño de los sistemas y se analizan sus respectivas complejidad computacionales1 Introducción 13 2 Presentación en Eventos y Publicaciones 15 3 Las Wavelets. Implementación de algoritmos 17 3.1 Tipos de Transformada Wavelet 17 3.2 Filtros QMF y Paquetes Wavelet 22 3.3 Implementación de los Paquetes Wavelet (WP) 24 3.4 Implementación de la Transformada Wavelet Sobre-completa (OCWT) 37 4 Sistema de compresión de voz 43 4.1 Generalidades de los sistemas de compresión de voz 43 4.2 Sistema propuesto para la compresión de señales de voz 44 4.3 Descompresor 48 4.4 Implementación en el DSP 50 4.5 Desempeño de los sistemas 51 4.6 Conclusiones 54 5 Sistema de multiplexación de señales de voz 55 5.1 Panorama de los Sistemas de Multiplexación de Señales basados en Wavelets 55 5.2 Diagrama esquemático de la multiplexación por división de paquetes wavelet (WPDM) 56 5.3 Análisis de la sincronización del sistema WPDM 58 5.4 Sistema propuesto 61 5.5 Pruebas de Desempeño 64 5.6 Implementación en el DSP 79 5.7 Conclusiones 82 6 Sistema de encriptación de señales 83 6.1 Panorama de los Sistemas de Encriptación de Señales 83 6.2 Sistema de Encriptación Propuesto 86 6.3 Resultados y Pruebas de Desempeño 9

Noise reduction and source recognition of partial discharge signals in gas-insulated substation

Ph.DDOCTOR OF PHILOSOPH

Multimedia Applications of the Wavelet Transform

This dissertation investigates novel applications of the wavelet transform in the analysis and compression of audio, still images, and video. Most recently, some surveys have been published on the restoration of noisy audio signals. Based on these, we have developed a wavelet-based denoising program for audio signals that allows flexible parameter settings. The multiscale property of the wavelet transform can successfully be exploited for the detection of semantic structures in images: A comparison of the coefficients allows the extraction of a predominant structure. This idea forms the basis of our semiautomatic edge detection algorithm. Empirical evaluations and the resulting recommendations follow. In the context of the teleteaching project Virtual University of the Upper Rhine Valley (VIROR), many lectures were transmitted between remote locations. We thus encountered the problem of scalability of a video stream for different access bandwidths in the Internet. A substantial contribution of this dissertation is the introduction of the wavelet transform into hierarchical video coding and the recommendation of parameter settings based on empirical surveys. Furthermore, a prototype implementation proves the principal feasibility of a wavelet-based, nearly arbitrarily scalable application. Mathematical transformations constitute a commonly underestimated problem for students in their first semesters of study. Motivated by the VIROR project, we spent a considerable amount of time and effort on the exploration of approaches to enhance mathematical topics with multimedia; both the technical design and the didactic integration into the curriculum are discussed. In a large field trial on "traditional teaching versus multimedia-enhanced teaching", the objective knowledge gained by the students was measured. This allows us to objectively rate positive the efficiency of our teaching modules