第1页 / 共258页
第2页 / 共258页
第3页 / 共258页
第4页 / 共258页
第5页 / 共258页
第6页 / 共258页
第7页 / 共258页
第8页 / 共258页
高阶谱书Higher-Order Spectral Analysis Toolbox.pdf
About the Authors
Ananthram Swami
Jerry M. Mendel
Chrysostomos L. (Max) Nikias
About the Authors
Tutorial
Introduction
Polyspectra and Linear Processes
Introduction
Definitions
Why Do We Need Higher-Order Statistics?
Bias and Variance of an Estimator
Estimating Cumulants
Examples
Estimating Polyspectra and Cross-polyspectra
Estimating the Power Spectrum
Estimating Bispectra and Cross-Bispectra
Examples
Examples
Estimating Bicoherence
Examples
Testing for Linearity and Gaussianity
Examples
Parametric Estimators, ARMA Models
MA Models
Examples
AR Models
Examples
ARMA Models
Examples
AR Order Determination
Examples
MA Order Determination
Examples
Linear Processes: Impulse Response Estimation
The Polycepstral Methods
Examples
Examples
The Matsuoka-Ulrych Algorithm
Examples
Linear Processes: Theoretical Cumulants and Polysp...
Examples
Summary
Linear Prediction Models
Levinson Recursion
Trench Recursion
Examples
Deterministic Formulation of FBLS
Adaptive Linear Prediction
RIV Algorithm: Transversal Form
Examples
RIV Algorithm: Double-Lattice Form
Examples
Summary
Harmonic Processes and DOA
Resolution and Variance
AR and ARMA Models
Pisarenko’s Method
Multiple Signal Classification (MUSIC)
Minimum-Norm Method
ESPRIT
Criterion-Based Estimators
Cumulant-Based Estimators
Examples
Examples
Summary
Nonlinear Processes
Solution Using Cross-Bispectra
Examples
Solution Using FTs
Examples
Quadratic Phase Coupling
Examples
Summary
Time-Frequency Distributions
Wigner Spectrum
Examples
Examples
Wigner Bispectrum
Examples
Examples
Wigner Trispectrum
Examples
Examples
Summary
Time-Delay Estimation
A Cross-Correlation Based Method
Examples
A Cross-Cumulant Based Method
Examples
A Hologram Based Method
Examples
Summary
Case Studies
Sunspot Data
Canadian Lynx Data
Examples
A Classification Example
Laughter Data
Pitfalls and Tricks of the Trade
Data Files
References
Reference
Function Tables
Higher-Order Spectrum Estimation: Conventional Met...
Higher-Order Spectrum Estimation: Parametric Metho...
Quadratic Phase Coupling (QPC)
Second-Order Volterra Systems
Harmonic Retrieval
Time-Delay Estimation (TDE)
Array Processing: Direction of Arrival (DOA)
Adaptive Linear Prediction
Impulse Response (IR), Magnitude and Phase Retriev...
Time-Frequency Estimates
Utilities
Demo
Miscellaneous
Prompting
Guided tour
Addenda
armaqs
armarts
armasyn
arorder
arrcest
biceps
bicepsf
bicoher
bicoherx
bispecd
bispecdx
bispeci
bispect
cum2x
cum3x
cum4x
cumest
cumtrue
doa
doagen
glstat
harmest
harmgen
hosademo
hosahelp
hprony
ivcal
maest
maorder
matul
nlgen
nlpow
nltick
pickpeak
qpcgen
qpctor
rivdl
rivtr
rpiid
tde
tdeb
tdegen
tder
tls
trench
trispect
wig2
wig2c
wig3
wig3c
wig4
wig4c
Higher-Order Spectral
Analysis Toolbox
For Use with MATLAB®
Ananthram Swami
Jerry M. Mendel
Chrysostomos L. (Max) Nikias
Computation
Visualization
Programming
User’s Guide
Version 2
%
FAX)
@
How to Contact The MathWorks:
508-647-7000
508-647-7001
The MathWorks, Inc.
24 Prime Park Way
Natick, MA 01760-1500
Phone
Fax
Mail
http://www.mathworks.com Web
ftp.mathworks.com
comp.soft-sys.matlab
Anonymous FTP server
Newsgroup
support@mathworks.com
suggest@mathworks.com
bugs@mathworks.com
doc@mathworks.com
subscribe@mathworks.com
service@mathworks.com
info@mathworks.com
Technical support
Product enhancement suggestions
Bug reports
Documentation error reports
Subscribing user registration
Order status, license renewals, passcodes
Sales, pricing, and general information
Higher-Order Spectral Analysis Toolbox User’s Guide
COPYRIGHT 1984 - 1998 by The MathWorks, Inc. All Rights Reserved.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro-
duced in any form without prior written consent from The MathWorks, Inc.
U.S. GOVERNMENT: If Licensee is acquiring the Programs on behalf of any unit or agency of the U.S.
Government, the following shall apply: (a) For units of the Department of Defense: the Government shall
have only the rights specified in the license under which the commercial computer software or commercial
software documentation was obtained, as set forth in subparagraph (a) of the Rights in Commercial
Computer Software or Commercial Software Documentation Clause at DFARS 227.7202-3, therefore the
rights set forth herein shall apply; and (b) For any other unit or agency: NOTICE: Notwithstanding any
other lease or license agreement that may pertain to, or accompany the delivery of, the computer software
and accompanying documentation, the rights of the Government regarding its use, reproduction, and disclo-
sure are as set forth in Clause 52.227-19 (c)(2) of the FAR.
MATLAB, Simulink, Handle Graphics, and Real-Time Workshop are registered trademarks and Stateflow
and Target Language Compiler are trademarks of The MathWorks, Inc.
Other product or brand names are trademarks or registered trademarks of their respective holders.
Printing History: May 1993
First printing
September 1995 Second printing
January 1998
Third printing
Contents
About the Authors
Tutorial
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Polyspectra and Linear Processes . . . . . . . . . . . . . . . . . . . . . . 1-4
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Why Do We Need Higher-Order Statistics? . . . . . . . . . . . . . . . 1-10
Bias and Variance of an Estimator . . . . . . . . . . . . . . . . . . . . . 1-11
Estimating Cumulants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
Estimating Polyspectra and Cross-polyspectra . . . . . . . . . . . . 1-15
Estimating the Power Spectrum . . . . . . . . . . . . . . . . . . . . . 1-15
Estimating Bispectra and Cross-Bispectra . . . . . . . . . . . . . 1-16
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-19
Estimating Bicoherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-20
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-20
Testing for Linearity and Gaussianity . . . . . . . . . . . . . . . . . . . 1-22
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-24
i
Parametric Estimators, ARMA Models . . . . . . . . . . . . . . . . . . 1-26
MA Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-29
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-30
AR Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-32
ARMA Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-32
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-34
AR Order Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-34
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-35
MA Order Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-36
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-37
Linear Processes: Impulse Response Estimation . . . . . . . . . . . 1-37
The Polycepstral Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-38
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-39
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-41
The Matsuoka-Ulrych Algorithm . . . . . . . . . . . . . . . . . . . . . 1-41
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-42
Linear Processes: Theoretical Cumulants and Polyspectra . . 1-43
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-43
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-45
Linear Prediction Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-47
Levinson Recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-47
Trench Recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-49
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-50
Deterministic Formulation of FBLS . . . . . . . . . . . . . . . . . . . . . 1-53
Adaptive Linear Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-54
RIV Algorithm: Transversal Form . . . . . . . . . . . . . . . . . . . . 1-56
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-57
RIV Algorithm: Double-Lattice Form . . . . . . . . . . . . . . . . . . 1-58
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-60
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-61
Harmonic Processes and DOA . . . . . . . . . . . . . . . . . . . . . . . . . 1-62
Resolution and Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-65
AR and ARMA Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-66
Pisarenko’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-67
Multiple Signal Classification (MUSIC) . . . . . . . . . . . . . . . . . . 1-68
Minimum-Norm Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-69
ESPRIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-70
ii
Contents
Criterion-Based Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-72
Cumulant-Based Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-74
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-75
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-77
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-79
Nonlinear Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-80
Solution Using Cross-Bispectra . . . . . . . . . . . . . . . . . . . . . . . . 1-80
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-82
Solution Using FTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-82
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-83
Quadratic Phase Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-84
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-87
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-88
Time-Frequency Distributions . . . . . . . . . . . . . . . . . . . . . . . . 1-89
Wigner Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-90
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-93
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-94
Wigner Bispectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-94
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-96
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-97
Wigner Trispectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-98
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-99
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-100
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-100
Time-Delay Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-101
A Cross-Correlation Based Method . . . . . . . . . . . . . . . . . . . . . 1-101
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-103
A Cross-Cumulant Based Method . . . . . . . . . . . . . . . . . . . . . . 1-103
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-105
A Hologram Based Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-105
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-107
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-107
iii
Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-108
Sunspot Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-108
Canadian Lynx Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-114
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-114
A Classification Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120
Laughter Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-122
Pitfalls and Tricks of the Trade . . . . . . . . . . . . . . . . . . . . . . . . 1-131
Data Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-134
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
2
Reference
Function Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
Higher-Order Spectrum Estimation: Conventional Methods . . 2-2
Higher-Order Spectrum Estimation: Parametric Methods . . . . 2-3
Quadratic Phase Coupling (QPC) . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Second-Order Volterra Systems . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
Harmonic Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
Time-Delay Estimation (TDE) . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
Array Processing: Direction of Arrival (DOA) . . . . . . . . . . . . . . 2-4
Adaptive Linear Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
Impulse Response (IR), Magnitude and
Phase Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
Time-Frequency Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
Demo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
Prompting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
Guided tour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
Addenda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
iv
Contents
About the Authors
About the Authors
About the Authors
Ananthram Swami
Ananthram Swami received his B.Tech, M.S. and Ph.D. degrees in electrical
engineering from the Indian Institute of Technology at Bombay, Rice
University, and the University of Southern California, respectively. He has
held positions with Unocal, USC, CS-3 and Malgudi Systems. He is currently
a Senior SCEEE Research Fellow at the Army Research Lab, Adelphi, MD.
Dr. Swami has published over fifty journal and conference papers in the areas
of modeling and parameter estimation of non-Gaussian processes. He is
co-organizer and co-chair of the Eighth IEEE Signal Processing Workshop on
Statistical Signal and Array Processing, Corfu, Greece (June 1996).
Jerry M. Mendel
Jerry Mendel received his B.S. degree in Mechanical Engineering in 1959, his
M.S. in 1960, and his Ph.D. in 1963 in Electrical Engineering from the
Polytechnic Institute of Brooklyn, NY. Currently he is Professor of Electrical
Engineering at USC in Los Angeles.
Dr. Mendel is a Fellow of the IEEE, a Distinguished Member of the IEEE
Control Systems Society, a member of Tau Beta Pi, Pi Tau Sigma, and Sigma
Xi, and a registered Professional Control Systems Engineer in California. He
has authored more than 300 technical papers, three textbooks and four other
books related to his research in estimation theory, deconvolution, higher-order
statistics, neural networks and fuzzy logic.
Chrysostomos L. (Max) Nikias
Chrysostomos L. (Max) Nikias received his B.S. degree in Electrical and
Mechanical Engineering from the National Technical University of Athens,
Greece and his M.S. and Ph.D. degrees in Electrical Engineering from the State
University of New York at Buffalo in 1980 and 1982. Currently he is a
Professor of Electrical Engineering at USC in Los Angeles, where he is also
Director of CRASP and Associate Dean of Academic Research.
Dr. Nikias is a Fellow of the IEEE. He is the author of over 150 journal and
conference papers, two textbooks, a monograph, and four patents. He is
co-author of the textbook Higher-Order Spectral Analysis: A Nonlinear Signal
Processing Framework, Prentice-Hall, Inc. 1993.
vi
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
