1 Introduction to Wavelets 2 A Multiresolution Formulation of Wavelet Systems 3 Filter Banks and the Discrete Wavelet Transform 4 Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases 5 The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients 6 Regularity, Moments, and Wavelet System Design 7 Generalizations of the Basic Multiresolution Wavelet System 8 Filter Banks and Transmultiplexers 9 Calculation of the Discrete Wavelet Transform 10 Wavelet-Based Signal Processing and Applications 11 Summary Overview 12 References Bibliography Appendix A Derivations for Chapter 5 on Scaling Functions Appendix B Derivations for Section on Properties Appendix C Matlab Programs Index

Introduction to Wavelets and Wavelet Transforms: A Primer

WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

From the Publisher:
Orthogonal frequency-division multiplexing (OFDM) is a method of digital modulation in which a signal is split into several narrowband channels at different frequencies.
CDMA is a form of multiplexing, which allows numerous signals to occupy a single transmission channel, optimising the use of available bandwidth. Multiplexing is sending multiple signals or streams of information on a carrier at the same time in the form of a single, complex signal and then recovering the separate signals at the receiving end.
Multi-Carrier (MC) CDMA is a combined technique of Direct Sequence (DS) CDMA (Code Division Multiple Access) and OFDM techniques. It applies spreading sequences in the frequency domain.
Wireless communications has witnessed a tremendous growth during the past decade and further spectacular enabling technology advances are expected in an effort to render ubiquitous wireless connectivity a reality.
This technical in-depth book is unique in its detailed exposure of OFDM, MIMO-OFDM and MC-CDMA. A further attraction of the joint treatment of these topics is that it allows the reader to view their design trade-offs in a comparative context.
Divided into three main parts:
Part I provides a detailed exposure of OFDM designed for employment in various applications
Part II is another design alternative applicable in the context of OFDM systems where the channel quality fluctuations observed are averaged out with the aid of frequency-domain spreading codes, which leads to the concept of MC-CDMA
Part III discusses how to employ multiple antennas at the base station for the sake of supporting multiple users in the uplink
Portrays theentire body of knowledge currently available on OFDMProvides the first complete treatment of OFDM, MIMO(Multiple Input Multiple Output)-OFDM and MC-CDMAConsiders the benefits of channel coding and space time coding in the context of various application examples and features numerous complete system design examplesConverts the lessons of Shannon's information theory into design principles applicable to practical wireless systemsCombines the benefits of a textbook with a research monograph where the depth of discussions progressively increase throughout the book

This all-encompassing self-contained treatment will appeal to researchers, postgraduate students and academics, practising research and development engineers working for wireless communications and computer networking companies and senior undergraduate students and technical managers.

OFDM and MC-CDMA for Broadband Multi-User Communications, WLANs and Broadcasting

A windscreen wiper device comprising an elastic, elongated carrier element, as well as an elongated wiper blade of a flexible material, which can be placed in abutment with a windscreen to be wiped, which wiper blade includes opposing longitudinal grooves on its longitudinal sides, in which grooves spaced-apart longitudinal strips of the carrier element are disposed, wherein neighboring ends of said longitudinal strips are interconnected by a respective connecting piece, which windscreen wiper device comprises a connecting device for an oscillating wiper arm, as well as a spoiler, a special feature of which is that the spoiler as a separate constructional element is detachably connected to the wiper blade.

Windscreen wiper device

There is a need, for example in electronic surveillance, to determine the modulation type of an incoming signal. The use of the wavelet transform for modulation identification of digital signals is described. The wavelet transform can effectively extract the transient characteristics in a digital communication signal, yielding distinct patterns for simple identification. Three identifiers for classifying PSK and FSK, M-ary PSK and M-ary FSK are considered. Statistics for hypothesis testing are derived. When the carrier-to-noise ratio is low, the symbol period and synchronisation time are needed to improve identification accuracy. A method for estimating them from the wavelet transform coefficients is included. The performance of the identifier is investigated through simulations.

Modulation identification of digital signals by the wavelet transform

The problem of estimating the time delay and the Doppler stretch for wideband signals from a moving target is considered. The Cramer-Rao bound and the maximum likelihood (ML) method of estimation are derived. Due to the uncertainty of the reflection coefficient, the ML method may not be practicable. An alternative method involving the location of the peak of the wideband ambiguity function of the signal is suggested. The performance of the method is analysed, and, under high signal-to-noise ratios (SNRs), the method is asymptotically unbiased, and the variances of the estimates are closed to the Cramer-Rao bound for a large variety of signals. Optimum signals for the joint estimation of the time delay and the Doppler stretch under practical constraints are designed and, through computer simulations, their performance are shown to be superior to the commonly used signals. >

The estimation of time delay and Doppler stretch of wideband signals

Wavelet packet division multiplexing (WPDM) is a multiple signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission. The overlapping nature of such waveforms in time and frequency provides a capacity improvement over the commonly used frequency division multiplexing (FDM) and time division multiplexing (TDM) schemes while their orthogonality properties ensure that the overlapping message signals can be separated by a simple correlator receiver. The interference caused by timing offset in transmission is examined. A design procedure that exploits the inherent degrees of freedom in the WPDM structure to mitigate the effects of timing error is introduced, and a waveform that minimizes the energy of the timing error interference is designed. An expression for the probability of error due to the presence of Gaussian noise and timing error for the transmission of binary data is derived. The performance advantages of the designed waveform over standard wavelet packet basis functions are demonstrated by both analytical and simulation methods. The capacity improvement of WPDM, its simple implementation, and the possibility of having optimum waveform designs indicate that WPDM holds considerable promise as a multiple signal transmission technique.

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Wavelet packet division multiplexing and wavelet packet design under timing error effects

Wavelet packet-division multiplexing (WPDM) is a high-capacity, flexible, and robust multiple-signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission. We derive an expression for the probability of error for a WPDM scheme in the presence of both impulsive and Gaussian noise sources and demonstrate that WPDM can provide greater immunity to impulsive noise than both a time-division multiplexing scheme and an orthogonal frequency-division multiplexing scheme.

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Performance of wavelet packet-division multiplexing in impulsive and Gaussian noise

The application of multirate filter banks in echo cancellation is investigated. The multiresolution algorithm is used to decompose the received sampling sequence into a number of components, and then, an adaptive algorithm is applied to cancel the echo in the received signal. In this paper, the performance of this method is discussed, from which optimal conditions for echo cancellation are established for the design of wavelet packet multiresolution decomposition. An efficient algorithm for designing such a set of optimal discrete filter banks is developed. The cases of optimal in-band and adjacent-band adaptive filtering are examined. Experimental results showed that the use of optimally designed multiresolution filter banks coupled with in-band or adjacent-band adaptive filtering is much more effective than the employment of commonly used wavelet filter banks. Furthermore, the use of the adjacent-band adaptive filtering algorithm has superior performance compared with that of the in-band filtering.

Optimum filter banks for signal decomposition and its application in adaptive echo cancellation

The problem of joint estimation of time delay and Doppler shift is considered from the point of view of the Wigner distribution of the signal. A very efficient method of obtaining the optimum signal with minimum estimation error based on the convexity of the design region is developed. Practical applications, however, require the signal to satisfy other constraints which present complications in acquiring the optimum signal. A design approach based on the method of simulated annealing is suggested to solve for the optimum signal under constraints. The performance of the signals so obtained is evaluated and compared with that of signals obtained by synthesis. >

Qu Jin

Papers

The estimation of time delay and Doppler stretch of wideband signals

Wavelet packet division multiplexing and wavelet packet design under timing error effects

Performance of wavelet packet-division multiplexing in impulsive and Gaussian noise

Optimum filter banks for signal decomposition and its application in adaptive echo cancellation

Design of optimum signals for the simultaneous estimation of time delay and Doppler shift