Fundamentals of Signal Processing

Fundamentals of Signal Processing tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả các lĩn...

A Wavelet Tour of Signal Processing St´ephane Mallat [...]... nd a criterion for selecting a basis that is intrinsically well adapted to represent a class of signals Mathematical approximation theory suggests choosing a basis that can construct precise signal approximations with a linear combination of a small number of vectors selected inside the basis These selected vectors can be interpreted as intrinsic signal structures Compact coding and signal estimation... leaves aside many information -processing applications The world of transients is considerably larger and more complex than the garden of stationary signals The search for an ideal Fourierlike basis that would simplify most signal processing is therefore a hopeless quest Instead, a multitude of di erent transforms and bases have proliferated, among which wavelets are just one example This book gives a. .. operator L ampli es or attenuates each sinusoidal component ei!t ^ of f by h(!) It is a frequency ltering of f As long as we are satis ed with linear time-invariant operators, the Fourier transform provides simple answers to most questions Its richness makes it suitable for a wide range of applications such as signal transmissions or stationary signal processing However, if we are interested in transient... signal variations By traveling through scales, zooming procedures provide powerful characterizations of signal structures such as singularities More and more bases Many orthonormal bases can be designed with fast computational algorithms The discovery of lter banks and wavelet bases has created a popular new sport of basis hunting Families of orthogonal bases are created every day This game may however... complex signals such as images Chapter 10 is rewritten and expanded to explain and compare the Bayes and minimax points of view Bounded Variation Signals Wavelet transforms provide sparse representations of piecewise regular signals The total variation norm gives an intuitive and precise mathematical framework in which to characterize the piecewise regularity of signals and images In this second edition,... interval that is shifted towards high frequencies Multiscale Zooming The wavelet transform can also detect and characterize transients with a zooming procedure across scales Suppose that is real Since it has a zero average, a wavelet coe cient Wf (u s) measures the variation of f in a neighborhood of u whose size is proportional to s Sharp signal transitions create large amplitude wavelet coe cients Chapter... algorithms are examples of adaptive transforms that construct sparse representations Fundamentals of Signal Processing Fundamentals of Signal Processing Bởi: Minh N Do Outline Foundations Signals Represent Information Introduction to Systems Discrete-Time Signals and Systems Linear Time-Invariant Systems Discrete-Time Convolution Review of Linear Algebra Hilbert Spaces Signal Expansions Fourier Analysis 10 Continuous-Time Fourier Transform (CTFT) 11 Discrete-Time Fourier Transform (DTFT) 12 DFT as a Matrix Operation 13 The FFT Algorithm 14 Solutions Sampling and Frequency Analysis Introduction Proof Illustrations Sampling and Reconstruction with Matlab Systems View of Sampling and Reconstruction Sampling CT Signals: A Frequency Domain Perspective The DFT: Frequency Domain with a Computer Analysis Discrete-Time Processing of CT Signals Short Time Fourier Transform 10 Spectrograms 11 Filtering with the DFT 12 Image Restoration Basics 13 Solutions 1/2 Fundamentals of Signal Processing Digital Filtering Difference Equation 103 The Z Transform: Definition Table of Common z-Transforms Understanding Pole/Zero Plots on the Z-Plane Filtering in the Frequency Domain Linear-Phase FIR Filters Filter Structures Overview of Digital Filter Design Window Design Method 125 10 Frequency Sampling Design Method for FIR Filters 11 Parks-McClellan FIR Filter Design 12 FIR Filter Design using MATLAB 13 MATLAB FIR Filter Design Exercise 14 Solutions Statistical and Adaptive Signal Processing Introduction to Random Signals and Processes Stationary and Nonstationary Random Processes Random Processes: Mean and Variance Correlation and Covariance of a Random Signal Autocorrelation of Random Processes Crosscorrelation of Random Processes Introduction to Adaptive Filters Discrete-Time, Causal Wiener Filter Practical Issues in Wiener Filter Implementation 10 Quadratic Minimization and Gradient Descent 11 The LMS Adaptive Filter Algorithm 12 First Order Convergence Analysis of the LMS Algorithm 13 Adaptive Equalization Solutions Glossary Bibliography Index Detail here Fundamentals of Signal Processing 2/2 '7 A WAVELET TOUR OF SIGNAL PROCESSING A WAVELET TOUR OF SIGNAL PROCESSING Second Edition Stephane Mallat &cole Polytechnique, Paris Courant Institute, New York University W ACADEMIC PRESS A Harcourt Science and Technology Company San Diego San Francisco New York Boston London Sydney Tokyo This book is printed on acid-free paper. @ Copyright 0 1998,1999, Elsevier (USA) All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing fi-om the publisher. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida 32887-6777. Academic Press An imprint of Elsevier 525 B Street, Suite 1900, San Diego, California 92101-4495, USA http://www.academicpress.com Academic Press 84 Theobald’s Road, London WClX 8RR, UK http ://m .academicpress. corn ISBN: 0-12-466606-X A catalogue record for this book is available from the British Library Produced by HWA Text and Data Management, Tunbridge Wells Printed in the United Kingdom at the University Press, Cambridge PRINTED IN THE UNITED STATES OF AMERICA 03 04 05 06 987654 A mes parents, Alexandre et Francine Contents PREFACE xv PREFACE TO THE SECOND EDITION xx NOTATION xxii INTRODUCTION TO A TRANSIENT WORLD I. I Fourier Kingdom I .2 Time-Frequency Wedding I .2. I I .2.2 Wavelet Transform Bases of Time-Frequency Atoms I .3. I I .3.2 I .4. I Approximation I .4.2 Estimation I .4.3 Compression I .5. I I .5.2 Road Map Windowed Fourier Transform I .3 Wavelet Bases and Filter Banks Tilings of Wavelet Packet and Local Cosine Bases I .4 Bases for What? I .5 Travel Guide Reproducible Computational Science vii 2 2 3 4 6 7 9 11 12 14 16 17 17 18 [...]... “optimal” linear procedures, and fast algorithms are available PREFACE xvii WAVELAB LASTWAVE and Toolboxes Numerical experimentations are necessary to fully understand the algorithms and theorems in this book To avoid the painful programming of standard procedures, nearly all wavelet and time-frequency algorithms are available in the WAVELAB package, programmed in M~TLAB WAVELAB is a freeware software... 577 585 587 Appendix A MATHEMATICAL COMPLEMENTS A I Functions and Integration A 2 Banach and Hilbert Spaces A 3 Bases of Hilbert Spaces A. 4 A. 5 Linear Operators Separable Spaces and Bases 59 1 593 595 596 598 XiV CONTENTS A 6 Random Vectors and Covariance Operators A. 7 Dims 599 60 1 Appendix B SOFTWARE TOOLBOXES 603 609 610 B.1 WAVELAB B.2 LASTWAVE B.3 Freeware Wavelet Toolboxes BIBLIOGRAPHY INDEX 6I2... construction of sparse representations with orthonormalbases, and study applicationsof non-linear diagonal operators in these bases It may start in Chapter 10 with a comparison of linear and non-linear operatorsused to estimate piecewiseregular signals contaminatedby a white noise A quick excursion in Chapter 9 introduces linear and non-linear approximations to explain what is a sparse representation Wavelet. .. Yet, classical signal processing has devoted most of its efforts to Fundamentals of Image Processing hany.farid@dartmouth.edu http://www.cs.dartmouth.edu/ ~ farid 0. Mathematical Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.1: Vectors 0.2: Matrices 0.3: Vector Spaces 0.4: Basis 0.5: Inner Products and Projections [*] 0.6: Linear Transforms [*] 1. Discrete-Time Signals and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14 1.1: Discrete-Time Signals 1.2: Discrete-Time Systems 1.3: Linear Time-Invariant Systems 2. Linear Time-Invariant Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 2.1: Space: Convolution Sum 2.2: Frequency: Fourier Transform 3. Sampling: Continuous to Discrete (and back) . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1: Continuous to Discrete: Space 3.2: Continuous to Discrete: Frequency 3.3: Discrete to Continuous 4. Digital Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.1: Choosing a Frequency Response 4.2: Frequency Sampling 4.3: Least-Squares 4.4: Weighted Least-Squares 5. Photons to Pixels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.1: Pinhole Camera 5.2: Lenses 5.3: CCD 6. Point-Wise Operations . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.1: Lookup Table 6.2: Brightness/Contrast 6.3: Gamma Correction 6.4: Quantize/Threshold 6.5: Histogram Equalize 7. Linear Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 7.1: Convolution 7.2: Derivative Filters 7.3: Steerable Filters 7.4: Edge Detection 7.5: Wiener Filter 8. Non-Linear Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 8.1: Median Filter 8.2: Dithering 9. Multi-Scale Transforms [*] . . . . . . . . . . . . . . . . . . . . 63 10. Motion Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 10.1: Differential Motion 10.2: Differential Stereo 11. Useful Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 11.1: Expectation/Maximization 11.2: Principal Component Analysis [*] 11.3: Independent Component Analysis [*] [*] In progress 0. Mathematical Foundations 0.1 Vectors 0.2 Matrices 0.3 Vector Spaces 0.4 Basis 0.5 Inner Products and Projections 0.6 Linear Trans- forms 0.1 Vectors From the preface of Linear Algebra and its Applications: “Linear algebra is a fantastic subject. On the one hand it is clean and beautiful.” – Gilbert Strang This wonderful branch of mathematics is both beautiful and use- ful. It is the cornerstone upon which signal and image processing is built. This short chapter can not be a comprehensive survey of linear algebra; it is meant only as a brief introduction and re- view. The ideas and presentation order are modeled after Strang’s highly recommended Linear Algebra and its Applications. x y x+y=5 2x−y=1 (x,y)=(2,3) Figure 0.1 “Row” solu- tion (2,1) (−1,1) (1,5) (4,2) (−3,3) Figure 0.2 “Column” solution At the heart of linear algebra is machinery for solving linear equa- tions. In the simplest case, the number of unknowns equals the number of equations. For example, here are a two equations in two unknowns: 2x − y = 1 x + y = 5. (1) There are at least two ways in which we can think of solving these equations for x and y. The first is to consider each equation as describing a line, with the solution being at the intersection of the lines: in this case the point (2, 3), Figure 0.1. This solution is termed a “row” solution because the equations are considered in isolation of one another. This is in contrast to a “column” solution in which the equations are rewritten in vector form:  2 1  x +  −1 1  y =  1 5  . (2) The Hindawi Publishing Corporation EURASIP Journal on Embedded Systems Volume 2009, Article ID 598529, 13 pages doi:10.1155/2009/598529 Research Article An Open Framework for Rapid Prototyping of Signal Processing Applications Maxime Pelcat, 1 Jonathan Piat, 1 Matthieu Wipliez, 1 Slaheddine Aridhi, 2 and Jean-Franc¸oisNezan 1 1 IETR/Image and Remote Sensing Group, CNRS UMR 6164/INSA Rennes, 20, avenue des Buttes de Co ¨ esmes, 35043 Rennes Cedex, France 2 HPMP Division, Texas Instruments, 06271 Villeneuve Loubet, France Correspondence should be addressed to Maxime Pelcat, mpelcat@insa-rennes.fr Received 27 February 2009; Revised 7 July 2009; Accepted 14 September 2009 Recommended by Markus Rupp Embedded real-time applications in communication systems have significant timing constraints, thus requiring multiple computation units. Manually exploring the potential parallelism of an application deployed on multicore architectures is greatly time-consuming. This paper presents an open-source Eclipse-based framework which aims to facilitate the exploration and development processes in this context. The framework includes a generic graph editor (Graphiti), a graph transformation library (SDF4J) and an automatic mapper/scheduler tool with simulation and code generation capabilities (PREESM). The input of the framework is composed of a scenario description and two graphs, one graph describes an algorithm and the second graph describes an architecture. The rapid prototyping results of a 3GPP Long-Term Evolution (LTE) algorithm on a multicore digital signal processor illustrate both the features and the capabilities of this framework. Copyright © 2009 Maxime Pelcat et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction The recent evolution of digital communication systems (voice, data, and video) has been dramatic. Over the last two decades, low data-rate systems (such as dial-up modems, first and second generation cellular systems, 802.11 Wireless local area networks) have been replaced or augmented by systems capable of data rates of several Mbps, supporting multimedia applications (such as DSL, cable modems, 802.11b/a/g/n wireless local area networks, 3G, WiMax and ultra-wideband personal area networks). As communication systems have evolved, the resulting increase in data rates has necessitated a higher system algo- rithmic complexity. A more complex system requires greater flexibility in order to function with different protocols in different environments. Additionally, there is an increased need for the system to support multiple interfaces and multicomponent devices. Consequently, this requires the optimization of device parameters over varying constraints such as performance, area, and power. Achieving this device optimization requires a good understanding of the application complexity and the choice of an appropriate architecture to support this application. An embedded system commonly contains several pro- cessor cores in addition to hardware coprocessors. The embedded system designer needs to distribute a set of signal processing functions onto a given hardware with predefined features. The functions are then executed as software code on target architecture; this action will be called a deployment in this paper. A common approach to implement a parallel algorithm is the creation of a program containing several synchronized threads in which execution is driven by the scheduler of an operating system. Such an implementation does Fundamentals of Signal Processing Biên tập bởi: Minh N Do Fundamentals of Signal Processing Biên tập bởi: Minh N Do Các tác giả: Minh N Do Stephen Kruzick Don Johnson Phiên trực tuyến: http://voer.edu.vn/c/f2feed3c MỤC LỤC Introduction to Fundamentals of Signal Processing Foundations 2.1 Signals Represent Information 2.2 Introduction to Systems 2.3 Discrete-Time Signals and Systems 2.4 Systems in the Time-Domain 2.5 Discrete Time Convolution Tham gia đóng góp 1/25 Introduction to Fundamentals of Signal Processing What is Digital Signal Processing? To understand what is Digital Signal Processing (DSP) let’s examine what does each of its words mean “Signal” is any physical quantity that carries information “Processing” is a series of steps or operations to achieve a particular end It is easy to see that Signal Processing is used everywhere to extract information from signals or to convert information-carrying signals from one form to another For example, our brain and ears take input speech signals, and then process and convert them into meaningful words Finally, the word “Digital” in Digital Signal Processing means that the process is done by computers, microprocessors, or logic circuits The field DSP has expanded significantly over that last few decades as a result of rapid developments in computer technology and integrated-circuit fabrication Consequently, DSP has played an increasingly important role in a wide range of disciplines in science and technology Research and development in DSP are driving advancements in many high-tech areas including telecommunications, multimedia, medical and scientific imaging, and human-computer interaction To illustrate the digital revolution and the impact of DSP, consider the development of digital cameras Traditional film cameras mainly rely on physical properties of the optical lens, where higher quality requires bigger and larger system, to obtain good images When digital cameras were first introduced, their quality were inferior compared to film cameras But as microprocessors become more powerful, more sophisticated DSP algorithms have been developed for digital cameras to correct optical defects and improve the final image quality Thanks to these developments, the quality of consumer-grade digital cameras has now surpassed the equivalence in film cameras As further developments for digital cameras attached to cell phones (cameraphones), where due to small size requirements of the lenses, these cameras rely on DSP power to provide good images Essentially, digital camera technology uses computational power to overcome physical limitations We can find the similar trend happens in many other applications of DSP such as digital communications, digital imaging, digital television, and so on In summary, DSP has foundations on Mathematics, Physics, and Computer Science, and can provide the key enabling technology in numerous applications 2/25 Overview of Key Concepts in Digital Signal Processing The two main characters in DSP are signals and systems A signal is defined as any physical quantity that varies with one or more independent variables such as time (onedimensional signal), or space (2-D or 3-D signal) Signals exist in several types In the real-world, most of signals are continuous-time or analog signals that have values continuously at every value of time To be processed by a computer, a continuous-time signal has to be first sampled in time into a discrete-time signal so that its values at a discrete set of time instants can be stored in computer memory locations Furthermore, in order to be processed by logic circuits, these signal values have to be quantized in to a set of discrete values, and the final result is called a digital signal When the quantization effect is ignored, the terms discrete-time signal and digital signal can be used interchangeability In signal processing, a system is defined as a process whose input and output are signals An important class of systems is the .. .Fundamentals of Signal Processing Digital Filtering Difference Equation 103 The Z Transform: Definition Table of Common z-Transforms Understanding Pole/Zero... Adaptive Signal Processing Introduction to Random Signals and Processes Stationary and Nonstationary Random Processes Random Processes: Mean and Variance Correlation and Covariance of a Random Signal. .. 12 First Order Convergence Analysis of the LMS Algorithm 13 Adaptive Equalization Solutions Glossary Bibliography Index Detail here Fundamentals of Signal Processing 2/2