第1页 / 共463页
第2页 / 共463页
第3页 / 共463页
第4页 / 共463页
第5页 / 共463页
第6页 / 共463页
第7页 / 共463页
第8页 / 共463页
Random Signal Processing，Shaila Dinkar Apte，2018.(463s).pdf
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgments
About the Author
1. Introduction to Random Signals
Learning Objectives
1.1 Introduction to Set Theory
1.1.1 Union and Intersection
1.1.2 Algebra of Sets
1.1.3 De Morgan’s Laws
1.1.4 Duality Principle
Concept Check
1.2 Probability
1.2.1 Conditional Probability
1.2.2 Bayes’ Theorem
1.2.2.1 Alternative Statement of Bayes’ Theorem
1.2.3 Mutually Exclusive and Independent Events
Concept Check
1.3 Random Variable
1.3.1 Cumulative Distribution Function (CDF)
1.3.2 Probability Density Function (pdf)
Concept Check
1.4 Standard Distribution Functions
1.4.1 Probability Distribution Functions for Continuous Variables
1.4.2 Probability Distribution Functions for Discrete Variables
1.4.2.1 Permutations
1.4.2.2 Combinations
1.4.2.3 Bernoulli’s Trials
1.4.2.4 Binomial Distribution
1.4.2.5 Poisson Distribution
Concept Check
1.5 Central Limit Theorem, Chi-Square Test, and Kolmogorov–Smirnov Test
1.5.1 Central Limit Theorem
1.5.2 Computer Generation of a Gaussian Distributed Random Variable
1.5.3 Chi-Square Test
1.5.4 Kolmogorov–Smirnov Test
Concept Check
Summary
Key Terms
Multiple-Choice Questions
Review Questions
Problems
Answers
Multiple-Choice Questions
Problems
2. Properties of Random Variables
Learning Objectives
2.1 Statistical Properties of Random Variables
Concept Check
2.2 Functions for Finding Moments
Concept Check
2.3 Transformations of a Random Variable
2.3.1 Monotonic Transformations of a Random Variable
2.3.2 Multiple-Valued Transformations of a Random Variable
2.3.3 Computer Generation of a Transformed Variable
Concept Check
2.4 Computation of the Energy Density Spectrum of a Deterministic Signal
2.4.1 Estimation of Power Density Spectrum of Random Signal
2.4.2 Use of Discrete Fourier Transform (DFT) for Power Spectrum Estimation
Concept Check
Summary
Key Terms
Multiple-Choice Questions
Review Questions
Problems
Answers
Multiple-Choice Questions
Problems
3. Multiple Random Variables and Random Process
Learning Objectives
3.1 Multiple Random Variables
3.1.1 Marginal Density Functions and Statistical Independence
3.1.2 Operations on Multiple Random Variables
Concept Check
3.2 Modeling a Random Signal
3.2.1 AR, MA, and ARMA Modeling
Concept Check
3.3 Random Processes
3.3.1 Stationary and Nonstationary Process
3.3.2 Stationary Processes
3.3.3 N[sup(th)] Order or Strict Sense Stationary Process
Concept Check
Summary
Key Terms
Multiple-Choice Questions
Review Questions
Problems
Answers
Multiple-Choice Questions
Problems
4. Detection and Estimation
4.1 Basics of Communication Theory
4.1.1 Transmitter
4.1.1.1 Justicfiation for Sampling and Quantization of Analog Signals
4.1.2 Channel
4.1.3 Receiver
Concept Check
4.2 Linear but Time Varying Systems
4.2.1 Filter Characteristics of Linear Systems
4.2.2 Distortionless Transmission through a System
4.2.2.1 Signal Bandwidth
4.2.3 Ideal Low-Pass Filter, High-Pass Filter, and Bandpass Filter Characteristics
4.2.4 Causality and Paley–Wiener Criteria
4.2.4.1 Statement of the Theorem
4.2.5 Relation between Bandwidth and Rise Time
Concept Check
4.3 Optimum Detection
4.3.1 Weighted Probabilities and Hypothesis Testing
4.3.2 Bayes Criterion
4.3.3 Minimax Criterion
4.3.4 Neyman–Pearson Criterion
4.3.5 Receiver Operating Characteristics
Concept Check
4.4 Estimation Theory
Concept Check
Summary
Keywords
Multiple-Choice Questions
Review Questions
Answers
Multiple-Choice Questions
5. Fundamentals of Speech Processing
Learning Objectives
5.1 LTI and LTV Models for Speech Production
5.1.1 LTI Model for Speech
5.1.2 Nature of Speech Signal
5.1.3 LTV Model
Concept Check
5.2 Voiced and Unvoiced Decision-Making
Analysis of the MATLAB Program Output
Concept Check
5.3 Audio File Formats—Nature of .wav File
Concept Check
5.4 Extraction of Fundamental Frequency
5.4.1 Fundamental Frequency or Pitch Frequency
5.4.1.1 Autocorrelation Method for Finding Pitch Period of a Voiced Speech Segment
5.4.1.2 AMDF Method for Finding Pitch Period of a Voiced Speech Segment
5.4.2 Pitch Contour
5.4.3 Pitch Period Measurement in Spectral Domain
5.4.3.1 Spectral Autocorrelation Method for Pitch Measurement
5.4.4 Cepstral Domain
5.4.5 Pitch Period Measurement Using Cepstral Domain
5.4.5.1 Interpretation of the Result
5.4.5.2 Interpretation of the Result
Concept Check
5.5 Formants and Relation of Formants with LPC
5.5.1 Practical Considerations
Concept Check
5.6 Evaluation of Formants
5.6.1 Evaluation of Formants Using Cepstrum
5.6.1.1 Evaluation of Formants for Voiced Speech Segment
5.6.1.2 Evaluation of Formants for Unvoiced Segment
5.6.2 Evaluation of Formants Using the Log Spectrum
5.6.2.1 Evaluation of Formants for Voiced Speech Segment
5.6.2.2 Evaluation of Formants for Unvoiced Segment
Concept Check
5.7 Evaluation of MFCC
5.7.1 Homomorphic Processing
5.7.2 The Auditory System as a Filter Bank
5.7.3 Mel Frequency Cepstral Coefcfiients
Concept Check
5.8 Evaluation of LPC
5.8.1 Forward Linear Prediction
5.8.2 Autocorrelation Method
Concept Check
Summary
Key Terms
Multiple-Choice Questions
Review Questions
Problems
Answers
Multiple-Choice Questions
Problems
6. Spectral Estimation of Random Signals
Learning Objectives
6.1 Estimation of Density Spectrum
6.1.1 Classicfiation of Signals
6.1.2 Power Spectral Density and Energy Spectral Density
6.1.2.1 Computation of Energy Density Spectrum of Deterministic Signals
6.1.2.2 Estimation of Power Density Spectrum of Random Signals
Concept Check
6.2 Nonparametric Methods
6.2.1 Use of DFT for Power Spectrum Estimation
6.2.2 Bartlett Method
6.2.3 Welch Method
6.2.4 Blackman–Tukey Method
6.2.5 Performance Comparison of Nonparametric Methods
Concept Check
6.3 Parametric Methods
6.3.1 Power Spectrum Estimation Using AR Model Parameters
6.3.2 Burg’s Method for Power Spectrum Estimation (Maximum Entropy Method—MEM)
6.3.3 Power Spectrum Estimation Using ARMA Model
6.3.4 Power Spectrum Estimation Using MA Model
Concept Check
6.4 Other Spectral Estimation Methods
6.4.1 Minimum Variance Power Spectrum Estimation
6.4.2 Eigen Analysis Algorithm for Spectrum Estimation
Concept Check
6.5 Evaluation of Formants Using the Power Spectral Density Estimate
6.5.1 Interpretation of the Results
Concept Check
6.6 Evaluation of Cepstrum
6.7 Evaluation of Higher Order Spectra
6.7.1 Cumulant Spectra
6.7.1.1 Indirect Method
6.7.1.2 Direct Method
Concept Check
Summary
Key Terms
Multiple-Choice Questions
Review Questions
Problems
Suggested Projects
Answers
Multiple Choice Questions
Problems
7. Statistical Speech Processing
Learning Objectives
7.1 Measurement of Statistical Parameters of Speech
Concept Check
7.2 Dynamic Time Warping
7.2.1 Linear Time Warping
7.2.2 Dynamic Time Warping
7.3 Statistical Sequence Recognition for Automatic Speech Recognition (ASR)
7.3.1 Bayes Rule
7.3.2 Hidden Markov Model
Concept Check
7.4 Statistical Pattern Recognition and Parameter Estimation
7.4.1 Statistical Parameter Estimation
7.4.2 Acoustic Probability Estimation for ASR
Concept Check
7.5 VQ-HMM-Based Speech Recognition
7.5.1 HMM Specicfiation and Model Training
7.5.1.1 Forward Algorithm
7.5.1.2 Backward Algorithm
7.5.1.3 Viterbi Algorithm
7.5.1.4 Baum–Welch Algorithm
7.5.1.5 Posterior Decoding
Concept Check
7.6 Discriminant Acoustic Probability Estimation
7.6.1 Discriminant Training
7.6.2 Use of Neural Networks
Concept Check
Summary
Key Terms
Multiple-Choice Questions
Review Questions
Problems
Answers
Multiple-Choice Questions
8. Transform Domain Speech Processing
Learning Objectives
8.1 Short Segment Analysis of Speech
8.1.1 Pitch Synchronous Analysis of Speech
Concept Check
8.2 Use of Transforms
8.2.1 Discrete Cosine Transform
Concept Check
8.3 Applications of DCT for Speech Processing
8.3.1 Signal Coding
8.3.2 Signal Filtering
8.3.3 Sampling Rate Conversion and Resizing
8.3.4 Feature Extraction and Recognition
Concept Check
8.4 Short-Time Fourier Transform (STFT)
Concept Check
8.5 Wavelet Transform
Concept Check
8.6 Haar Wavelet and Multiresolution Analysis
8.6.1 Multiresolution Analysis
Concept Check
8.7 Daubechies Wavelets
8.7.1 Matrix Multiplication Method for Computation of WT
8.7.2 Number of Operations
8.7.3 Time Band Width Product
Concept Check
8.8 Some Other Standard Wavelets
8.8.1 Mexican Hat Function
8.8.2 A Modulated Gaussian
8.8.3 Spline and Battle–Lemarie Wavelets
8.8.4 Biorthogonal Wavelets
8.8.5 Cohen–Daubechies–Feauveau Family of Biorthogonal Spline Wavelets
8.8.6 Wavelet Packets
8.8.6 1 Full Wavelet Packet Decomposition
Concept Check
8.9 Applications of WT
8.9.1 Denoising Using DWT
8.9.2 Signal Compression
8.9.3 Signal Filtering
8.9.4 Sampling Rate Conversion
Concept Check
Summary
Key Terms
Multiple-Choice Questions
Review Questions
Problems
Suggested Projects
Answers
Multiple-Choice Questions
Problems
9. Image Processing Techniques
Learning Objectives
9.1 Image Representation and Spatial Filtering
9.1.1 Edge Detection Using Spatial Filtering
9.1.2 Laplacian Mask
9.1.3 Laplacian of Gaussian
Concept Check
9.2 Transformations on Image
9.2.1 Linear Transformations
9.2.2 Gray-Level Slicing
9.2.3 Bit-Plane Slicing
9.2.3 Nonlinear Transformations
9.3 Histogram Equalization
9.3.1 Histogram Evaluation
9.3.2 Mapping the pdf Value with CDF
9.3.3 Histogram Equalization
9.3.4 Statistical Image Processing
Concept Check
9.4 Transform Domain Image Processing
9.4.1 Image Processing Using DCT
9.4.2 Image Processing Using WT
Concept Check
Summary
Key Terms
Multiple-Choice Questions
Review Questions
Problems
Answers
Multiple-Choice Questions
Problems
10. Applications of Random Signal Processing
Learning Objectives
10.1 Case Study 1: Handwritten Character Recognition
10.1.1 Components of an OCR System
10.1.2 Challenges in Devanagari Handwriting Recognition
10.1.3 Tree Classicfiation Based on Structural Features
10.1.4 Recognition Using Neural Network
10.2 Case Study 2: Writer Identicfiation and Vericfiation
10.2.1 Introduction
10.2.2 Importance of Writer Identicfiation and Vericfiation
10.2.3 Main Factors Discriminating Handwritings
10.2.4 Factors Affecting Handwriting
10.2.4.1 System for Writer Identicfiation and Vericfiation
10.2.4.2 Handwriting Acquisition
10.2.4.3 Preprocessing
10.2.4.4 Feature Extraction
10.2.5 Off-Line English Handwriting Databases
10.2.5.1 Writer Vericfiation System
Index
Random Signal Processing
Random Signal Processing
Shaila Dinkar Apte
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the
accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products
does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular
use of the MATLAB® software.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2018 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid-free paper
International Standard Book Number-13: 978-1-4987-8199-2 (Hardback)
978-1-138-74627-5 (Paperback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been
made to publish reliable data and information, but the author and publisher cannot assume responsibility for the
validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the
copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to
publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let
us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or
utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including
photocopying, microfilming, and recording, or in any information storage or retrieval system, without written
permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://
www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA
01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users.
For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been
arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for
identification and explanation without intent to infringe.
Library of Congress Cataloging‑in‑Publication Data
Names: Apte, Shaila Dinkar, author.
Title: Random signal processing / Shaila Dinkar Apte.
Description: Boca Raton : CRC Press, 2018. | Includes bibliographical
references and index.
Identifiers: LCCN 2017013790| ISBN 9781498781992 (hardback : acid-free paper)
| ISBN 9781315155357 (ebook)
Subjects: LCSH: Signal processing. | Random variables.
Classification: LCC TK5102.9 .A678 2018 | DDC 621.382/2--dc23
LC record available at https://lccn.loc.gov/2017013790
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
My beloved husband late Shri Dinkar
My grand children
Aarohi, Shriya and Shreyas
and Shruti
My students from
W.C.E., Sangli.
R.S.C.O.E., Pune
Contents
Preface .............................................................................................................................................xv
Acknowledgments ...................................................................................................................... xix
About the Author ........................................................................................................................ xxi
1.2.3
1. Introduction to Random Signals .........................................................................................1
Learning Objectives .................................................................................................................1
Introduction to Set Theory ..........................................................................................1
1.1
Union and Intersection ...................................................................................3
1.1.1
Algebra of Sets ..................................................................................................4
1.1.2
1.1.3
De Morgan’s Laws ............................................................................................4
Duality Principle ..............................................................................................5
1.1.4
Concept Check..........................................................................................................................5
Probability ......................................................................................................................5
1.2
Conditional Probability...................................................................................7
1.2.1
1.2.2
Bayes’ Theorem ..............................................................................................12
1.2.2.1
Alternative Statement of Bayes’ Theorem ................................... 14
Mutually Exclusive and Independent Events ............................................ 16
Concept Check........................................................................................................................ 17
1.3
Random Variable ......................................................................................................... 18
Cumulative Distribution Function (CDF) .................................................. 18
1.3.1
1.3.2
Probability Density Function (pdf) ............................................................. 21
Concept Check........................................................................................................................25
1.4
Standard Distribution Functions ..............................................................................26
Probability Distribution Functions for Continuous Variables ................26
1.4.1
Probability Distribution Functions for Discrete Variables ......................33
1.4.2
Permutations ...................................................................................33
1.4.2.1
1.4.2.2
Combinations ..................................................................................34
Bernoulli’s Trials .............................................................................34
1.4.2.3
Binomial Distribution ....................................................................34
1.4.2.4
Poisson Distribution ......................................................................36
1.4.2.5
Concept Check........................................................................................................................ 39
Central Limit Theorem, Chi-Square Test, and Kolmogorov–Smirnov Test .......40
1.5
Central Limit Theorem .................................................................................40
1.5.1
Computer Generation of a Gaussian Distributed Random Variable ......40
1.5.2
Chi-Square Test ..............................................................................................42
1.5.3
1.5.4 Kolmogorov–Smirnov Test ...........................................................................43
Concept Check........................................................................................................................44
Summary .................................................................................................................................45
Key Terms ...............................................................................................................................46
Multiple-Choice Questions ...................................................................................................46
Review Questions ..................................................................................................................48
Problems ..................................................................................................................................48
vii
相关推荐
2023年江西萍乡中考道德与法治真题及答案.doc
2012年重庆南川中考生物真题及答案.doc
2013年江西师范大学地理学综合及文艺理论基础考研真题.doc
2020年四川甘孜小升初语文真题及答案I卷.doc
2020年注册岩土工程师专业基础考试真题及答案.doc
2023-2024学年福建省厦门市九年级上学期数学月考试题及答案.doc
2021-2022学年辽宁省沈阳市大东区九年级上学期语文期末试题及答案.doc
2022-2023学年北京东城区初三第一学期物理期末试卷及答案.doc
2018上半年江西教师资格初中地理学科知识与教学能力真题及答案.doc
2012年河北国家公务员申论考试真题及答案-省级.doc
2020-2021学年江苏省扬州市江都区邵樊片九年级上学期数学第一次质量检测试题及答案.doc
2022下半年黑龙江教师资格证中学综合素质真题及答案.doc
