Sparse Signal Processing Lab1

Sparse Signal Processing Lab1 tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả các lĩnh vự...

The Scientist and Engineer's Guide toDigital Signal ProcessingSecond Edition Be sure to visit the book’s website at:www.DSPguide.com The Scientist and Engineer's Guide toDigital Signal ProcessingSecond EditionbySteven W. SmithCalifornia Technical PublishingSan Diego, California Important Legal Information: Warning and DisclaimerThis book presents the fundamentals of Digital Signal Processing using examples from common science andengineering problems. While the author believes that the concepts and data contained in this book are accurate andcorrect, they should not be used in any application without proper verification by the person making the application.Extensive and detailed testing is essential where incorrect functioning could result in personal injury or damage toproperty. The material in this book is intended solely as a teaching aid, and is not represented to be an appropriateor safe solution to any particular problem. For this reason, the author, publisher, and distributors make nowarranties, express or implied, that the concepts, examples, data, algorithms, techniques, or programs containedin this book are free from error, conform to any industry standard, or are suitable for any application. The author,publisher, and distributors disclaim all liability and responsibility to any person or entity with respect to any lossor damage caused, or alleged to be caused, directly or indirectly, by the information contained in this book. If youdo not wish to be bound by the above, you may return this book to the publisher for a full refund.The Scientist and Engineer's Guide toDigital Signal ProcessingSecond EditionbySteven W. Smithcopyright © 1997-1999 by California Technical PublishingAll rights reserved. No portion of this book may be reproduced ortransmitted in any form or by any means, electronic or mechanical,without written permission of the publisher.ISBN 0-9660176-7-6 hardcoverISBN 0-9660176-4-1 paperbackISBN 0-9660176-6-8 electronicLCCN 97-80293California Technical PublishingP.O. Box 502407San Diego, CA 92150-2407To contact the author or publisher through the internet: website: DSPguide.com e-mail: Smith@DSPguide.comPrinted in the United States of America First Edition, 1997 Second Edition, 1999 vContents at a GlanceFOUNDATIONSChapter 1. The Breadth and Depth of DSP .1Chapter 2. Statistics, Probability and Noise 11Chapter 3. ADC and DAC 35Chapter 4. DSP Software .67FUNDAMENTALSChapter 5. Linear Systems 87Chapter 6. Convolution 107Chapter 7. Properties of Convolution .123Chapter 8. The Discrete Fourier Transform 141Chapter 9. Applications of the DFT 169Chapter 10. Fourier Transform Properties 185Chapter 11. Fourier Transform Pairs 209Chapter 12. The Fast Fourier Transform 225 Chapter 13. Continuous Signal Processing 243DIGITAL FILTERSChapter 14. Introduction to Digital Filters 261Chapter 15. Moving Average Filters .277Chapter 16. Windowed-Sinc Filters .285Chapter 17. Custom Filters 297Chapter 18. FFT Convolution 311Chapter 19. Sparse Signal Processing - Lab1 Sparse Signal Processing Lab1 Bởi: Trac Tran Lab materials Lab material can be found here 1/1 TEAM LinG INTRODUCTION TODIGITAL SIGNALPROCESSING ANDFILTER DESIGN INTRODUCTION TODIGITAL SIGNALPROCESSING ANDFILTER DESIGNB. A. ShenoiA JOHN WILEY & SONS, INC., PUBLICATION Copyright © 2006 by John Wiley & Sons, Inc. All rights reserved.Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.No part of this publication may be reproduced, stored in a retrieval system, or transmitted in anyform or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise,except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, withouteither the prior written permission of the Publisher, or authorization through payment of theappropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers,MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requeststo the Publisher for permission should be addressed to the Permissions Department, John Wiley &Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online athttp://www.wiley.com/go/permission.Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their bestefforts in preparing this book, they make no representations or warranties with respect to theaccuracy or completeness of the contents of this book and specifically disclaim any impliedwarranties of merchantability or fitness for a particular purpose. No warranty may be created orextended by sales representatives or written sales materials. The advice and strategies containedherein may not be suitable for your situation. You should consult with a professional whereappropriate. Neither the publisher nor author shall be liable for any loss of profit or any othercommercial damages, including but not limited to special, incidental, consequential, or otherdamages.For general information on our other products and services or for technical support, please contactour Customer Care Department within the United States at (800) 762-2974, outside the UnitedStates at (317) 572-3993 or fax (317) 572-4002.Wiley also publishes its books in a variety of electronic formats. Some content that appears in printmay not be available in electronic formats. For more information about Wiley products, visit ourweb site at www.wiley.com.Library of Congress Cataloging-in-Publication Data:ISBN-13 978-0-471-46482-2 (cloth)Printed in the United States of America.10987654321ISBN-100-471- 46482-1 (cloth) CONTENTSPreface xi1 Introduction 11.1 Introduction 11.2 Applications of DSP 11.3 Discrete-Time Signals 31.3.1 Modeling and Properties of Discrete-Time Signals 81.3.2 Unit Pulse Function 91.3.3 Constant Sequence 101.3.4 Unit Step Function 101.3.5 Real Exponential Function 121.3.6 Complex Exponential Function 121.3.7 Properties of cos(ω0n) 141.4 History of Filter Design 191.5 Analog and Digital Signal Processing 231.5.1 Operation of a Mobile Phone Network 251.6 Summary 28Problems 29References 302 Time-Domain Analysis and z Transform 322.1 A Linear, Time-Invariant System 322.1.1 Models of the Discrete-Time System 332.1.2 Recursive Algorithm 362.1.3 Convolution Sum 382.2 z Transform Theory 412.2.1 Definition 412.2.2 Zero Input and Zero State Response 49v viCONTENTS2.2.3 Linearity of the System 502.2.4 Time-Invariant System 502.3 Using z Transform to Solve Difference Equations 512.3.1 More Applications of z Transform 562.3.2 Natural Response and Forced Response 582.4 Solving Difference Equations Using the Classical Method 592.4.1 Transient Response and Steady-State Response 632.5 z Transform Method Revisited 642.6 Convolution Revisited 652.7 A Model from Other Models 702.7.1 Review of Model Generation 722.8 Stability 772.8.1 Jury–Marden Test 782.9 Solution Using MATLAB Functions 812.10 Summary 93Problems CHAPTER 1 Introduction 1.1 INTRODUCTION We are living in an age of information technology. Most of this technology is based on the theory of digital signal processing (DSP) and implementation of the theory by devices embedded in what are known as digital signal processors (DSPs). Of course, the theory of digital signal processing and its applications is supported by other disciplines such as computer science and engineering, and advances in technologies such as the design and manufacturing of very large scale integration (VLSI) chips. The number of devices, systems, and applications of digital signal processing currently affecting our lives is very large and there is no end to the list of new devices, systems, and applications expected to be introduced into the market in the coming years. Hence it is difficult to forecast the future of digital signal processing and the impact of information technology. Some of the current applications are described below. 1.2 APPLICATIONS OF DSP Digital signal processing is used in several areas, including the following: 1. Telecommunications. Wireless or mobile phones are rapidly replacing wired (landline) telephones, both of which are connected to a large-scale telecom- munications network. They are used for voice communication as well as data communications. So also are the computers connected to a different network that is used for data and information processing. Computers are used to gen- erate, transmit, and receive an enormous amount of information through the Internet and will be used more extensively over the same network, in the com- ing years for voice communications also. This technology is known as voice over Internet protocol (VoIP) or Internet telephony. At present we can transmit and receive a limited amount of text, graphics, pictures, and video images from Introduction to Digital Signal Processing and Filter Design, by B. A. Shenoi Copyright © 2006 John Wiley & Sons, Inc. 1 2 INTRODUCTION mobile phones, besides voice, music, and other audio signals—all of which are classified as multimedia—because of limited hardware in the mobile phones and not the software that has already been developed. However, the computers can be used to carry out the same functions more efficiently with greater memory and large bandwidth. We see a seamless integration of wireless telephones and com- puters already developing in the market at present. The new technologies being used in the abovementioned applications are known by such terms as CDMA, TDMA, 1 spread spectrum, echo cancellation, channel coding, adaptive equaliza- tion, ADPCM coding, and data encryption and decryption, some of which are used in the software to be introduced in the third-generation (G3) mobile phones. 2. Speech Processing. The quality of speech transmission in real time over telecommunications networks from wired (landline) telephones or wireless (cel- lular) telephones is very high. Speech recognition, speech synthesis, speaker verification, speech enhancement, text-to-speech translation, and speech-to-text dictation are some of the other applications of speech processing. 3. Consumer Electronics. We have already mentioned cellular or mobile phones. Then we have HDTV, digital cameras, digital phones, answering machines, fax and modems, music synthesizers, recording and mixing of music signals to produce CD and DVDs. Surround-sound entertainment systems includ- ing CD and DVD players, laser printers, copying machines, and scanners are found in many homes. But the TV set, PC, [...]... particular – and higher-order moments derived from the curvelet transform: wavelet scale 5, fourth-order moment curvelet band 1, second-order moment curvelet band 7, third- and fourth-order moments curvelet band 8, fourth-order moment curvelet band 11, fourth-order moment curvelet band 12, fourth-order moment curvelet band 16, fourth-order moment curvelet band 19, second- and fourth-order moments Our results... second-, third-, and fourth-order moments at each scale (hence variance, skewness, and kurtosis) So each image had 15 features For each of 19 bands resulting from the curvelet transform, we again determined the second-, third-, and fourth-order moments at each band (hence variance, skewness, and kurtosis) So each image had 57 features 13 14 Introduction to the World of Sparsity Figure 1.8 Sample images... imaging and signal processing in biology, medicine, and the life sciences generally; astronomy, physics, and the natural sciences; seismology and land use studies, as indicative subdomains from geology and geography in the earth sciences; materials science, metrology, and other areas of mechanical and civil engineering; image and video compression, analysis, and synthesis for movies and television; and. .. theory (Candes and Tao 2006; ` Donoho 2006a; Candes et al 2006b) Compressed sensing uses the prior knowledge that signals are sparse, whereas Shannon theory was designed for frequency band– limited signals By establishing a direct link between sampling and sparsity, compressed sensing has had a huge impact in many scientific fields such as coding and information theory, signal and image acquisition and processing, ... transform xi Notation Functions and Signals f (t) f (t) or f (t1 , , td ) f [k] f [k] or f [k, l, ] f¯ fˆ f∗ H (z) lhs = O(rhs) lhs ∼ rhs 1{condition} L2 ( ) 2( ) (H) 0 continuous-time function, t ∈ R d-dimensional continuous-time function, t ∈ Rd discrete-time signal, k ∈ Z, or kth entry of a finite-dimensional vector d-dimensional discrete-time signal, k ∈ Zd time-reversed version of f as a function... Dirac dictionary (also known as standard unit vector basis or Kronecker basis), position scale for the wavelet dictionary, translation-duration-frequency for cosine packets, and position-scale-orientation for the curvelet dictionary in two dimensions In discrete-time, finite-length signal processing, a dictionary is viewed as an N × T matrix whose columns are the atoms, and the atoms are considered as... Figure 1.2 (left) SAR image of Gulf of Oman region and The Scientist and Engineer's Guide toDigital Signal ProcessingSecond Edition Be sure to visit the book’s website at:www.DSPguide.com The Scientist and Engineer's Guide toDigital Signal ProcessingSecond EditionbySteven W. SmithCalifornia Technical PublishingSan Diego, California Important Legal Information: Warning and DisclaimerThis book presents the fundamentals of Digital Signal Processing using examples from common science andengineering problems. While the author believes that the concepts and data contained in this book are accurate andcorrect, they should not be used in any application without proper verification by the person making the application.Extensive and detailed testing is essential where incorrect functioning could result in personal injury or damage toproperty. The material in this book is intended solely as a teaching aid, and is not represented to be an appropriateor safe solution to any particular problem. For this reason, the author, publisher, and distributors make nowarranties, express or implied, that the concepts, examples, data, algorithms, techniques, or programs containedin this book are free from error, conform to any industry standard, or are suitable for any application. The author,publisher, and distributors disclaim all liability and responsibility to any person or entity with respect to any lossor damage caused, or alleged to be caused, directly or indirectly, by the information contained in this book. If youdo not wish to be bound by the above, you may return this book to the publisher for a full refund.The Scientist and Engineer's Guide toDigital Signal ProcessingSecond EditionbySteven W. Smithcopyright © 1997-1999 by California Technical PublishingAll rights reserved. No portion of this book may be reproduced ortransmitted in any form or by any means, electronic or mechanical,without written permission of the publisher.ISBN 0-9660176-7-6 hardcoverISBN 0-9660176-4-1 paperbackISBN 0-9660176-6-8 electronicLCCN 97-80293California Technical PublishingP.O. Box 502407San Diego, CA 92150-2407To contact the author or publisher through the internet: website: DSPguide.com e-mail: Smith@DSPguide.comPrinted in the United States of America First Edition, 1997 Second Edition, 1999 vContents at a GlanceFOUNDATIONSChapter 1. The Breadth and Depth of DSP .1Chapter 2. Statistics, Probability and Noise 11Chapter 3. ADC and DAC 35Chapter 4. DSP Software .67FUNDAMENTALSChapter 5. Linear Systems 87Chapter 6. Convolution 107Chapter 7. Properties of Convolution .123Chapter 8. The Discrete Fourier Transform 141Chapter 9. Applications of the DFT 169Chapter 10. Fourier Transform Properties 185Chapter 11. Fourier Transform Pairs