Higher-Order Spectral Analysis Toolbox – For Use with MATLAB

Higher-Order Spectral Analysis Toolbox – For Use with MATLAB
اسم المؤلف
Ananthram Swami, Jerry M. Mendel, Chrysostomos L. (Max) Nikias
التاريخ
19 سبتمبر 2022
المشاهدات
464
التقييم
(لا توجد تقييمات)
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Higher-Order Spectral Analysis Toolbox – For Use with MATLAB
Computation, Visualization, Programming
Ananthram Swami, Jerry M. Mendel, Chrysostomos L. (Max) Nikias
Contents
About the Authors
1 Tutorial
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 1-24ii Contents
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 1-70iii
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 . 1-107iv Contents
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
Index
A
adaptive filter
double lattice 2-72
RIV 2-74
adaptive linear prediction 1-54
ambiguity function 1-90-1-92
AR method
DOA 2-44
harmonic retrieval 2-50
AR models 1-31
order determination 1-34, 2-15
parameter estimation 2-17
parameter identifiability 1-31
ar1.mat 1-134
ARMA models 1-32
AR order estimation 2-15
AR parameter estimation 2-17
residual time series 2-12
arma1.mat 1-135
armaqs 1-33, 2-8
armarts 2-11
armasyn 2-14
arorder 2-15
arrcest 2-17
autocorrelation 1-6
B
backward prediction problem 1-47
beamformer 1-64, 1-65, 1-77
bibliography 1-139
biceps 2-19
bicepsf 2-21
bicepstrum 1-38
bicoher 2-23
bicoherence 1-4
auto 2-23
cross 2-25
estimation 1-20, 2-23
bicoherx 2-25
bispecd 2-27
bispecdx 2-29
bispeci 2-31
bispect 2-33
bispectrum 1-8
cross 2-29
direct estimate 1-19
direct method 2-27
estimation 1-17
indirect method 1-18, 2-31
theoretical 2-33
Wigner 2-90, 2-92
Burg’s maximum-entropy estimator 1-74
C
Canadian lynx data 1-114
Capon (ML) 1-74
Capon’s maximum-likelihood estimator 1-73
Choi-Williams
distributions 1-89
filter 1-92, 1-95, 1-100
smoothing 2-88
cross-bicoherence 1-10
cross-biperiodogram 1-17
cross-bispectra
Volterra systems 1-80
cross-bispectrum 1-9
direct estimate 1-18
direct method 2-29
estimation 1-13
indirect estimate 1-16
cross-cumulant 1-81Index
I-2
cum2x 2-34
cum3x 2-36
cum4x 2-38
cumest 2-40
cumtrue 2-42
cumulants 1-4
auto 2-40
definitions 1-6
fourth-order 2-40, 2-42
sample estimates 1-12
second-order 2-34, 2-40
third-order 2-36, 2-41
true 2-42
D
demos 2-54
DOA 1-62, 1-64
AR 1-74
beamformer 1-74
Capon(ML) 1-74
cumulant-based estimators 1-74
eigenvector 1-74
ESPRIT 1-74
fourth-order cumulants 2-44
minimum-norm 1-74
MUSIC 1-74
Pisarenko 1-74
spatial covariance matrix 2-44
doa 2-44
doa1.mat 1-135
doagen 2-46
E
eda 1-112, 1-114, 1-120
eigenvector method
DOA 2-44
harmonic retrieval 2-50
eigenvector methods 1-67
ESPRIT 1-70, 1-74
DOA 2-44
examples
AR order determination 1-34
AR parameter estimation 1-32
ARMA parameter estimation 1-34
bicepstrum-based IR estimation 1-39, 1-41
bicoherence estimation 1-20
computing true cumulants 1-43
cross-bicoherence estimation 1-20
cross-bispectrum 1-19
cumulant estimation 1-14
cumulation estimation 1-14
DOA estimation 1-77
Gaussianity-linearity tests 1-24
harmonic retrieval 1-75
Levinson recursion 1-50
MA order determination 1-37
MA parameter estimation 1-30
Matsuoka-Ulrych algorithm 1-42
QPC detection 1-87
RIV double-lattice form 1-60
RIV transversal form 1-57
speech signal 1-122
sunspot data 1-108
time-delay estimation 1-103, 1-105, 1-107
trench recursion 1-50
Volterra system identification 1-82, 1-83
Wigner bispectrum 1-96
smoothed 1-97
Wigner spectrum 1-93
smoothed 1-94
Wigner trispectrum 1-99
smoothed 1-100Index
I-3
F
FBLS 1-53
deterministic formulation 1-53
forward prediction problem 1-47
forward-backward least squares problem 1-54
frequency coupling 1-128
frequency estimation 1-65, 2-50
G
Gaussianity test 1-22, 2-47
gldat.mat 1-135
glstat 2-47
GM equations 1-29
guided tour 2-54
H
harm.mat 1-135
harmest 2-50
harmgen 2-53
harmonic retrieval 1-62, 1-64
AR models 1-66
ARMA models 1-66
cumulant-based method 1-74
minimum-norm method 1-69
MUSIC 1-68
Pisarenko’s method 1-67
synthetics 2-53
help 2-55
higher-order spectra 1-2
higher-order statistics 1-2
motivations 1-10
hologram
third order 1-106
hosademo 2-54
hosahelp 2-55
hprony 2-56
I
instrumental variables 2-57
ivcal 2-57
K
kurtosis 1-7
L
Levinson-Durbin recursion 1-48, 2-85
linear models
frequency-domain bicepstral method 2-21
lag-domain bicepstral method 2-19
linear prediction 1-31, 1-47
adaptive 1-54
linear processes
impulse response estimation 1-37
theoretical cumulants 1-43
theoretical polyspectra 1-43
linearity test 1-24
linearity tests 2-47
M
MA models 1-29
order estimation 2-61
parameters estimation 2-58
ma1.mat 1-135
maest 2-58
maorder 2-61
Matsuoka-Ulrych algorithm 2-63
matul 2-63
minimum phase 1-11
minimum-norm method
DOA 2-44
harmonic retrieval 2-50Index
I-4
mixed-phase 1-11, 1-135
ML-Capon 1-74
MUSIC 1-68
DOA 2-44
harmonic retrieval 2-50
N
nl1.mat 1-135
nl2.mat 1-136
nlgen 2-64
nlgen 2-64
nlpow 2-65
nltick 2-67
noise subspace 1-69
nonredundant region 1-133
normal equations
cumulant-based 2-17
deterministic 1-53
P
peak picking 2-69
periodogram 1-15, 1-64
phase coupling 1-84, 1-132
pickpeak 2-69
Pisarenko’s method 1-67
DOA 2-44
harmonic retrieval 2-50
pitfalls 1-131
polycepstra methods 1-38
polycepstral methods 1-38
polycepstrum 1-40
polyspectra
linear processes 1-4
windows 1-16
polyspectrum
definitions 1-6
power spectrum
Wigner 2-87
power spectrum estimation 1-4
conventional methods 1-15
criterion-based estimators 1-72
criterion-based methods 1-15
model-based methods 1-15
non-parametric methods 1-15
parametric estimators
ARMA models 1-26
power spectrum estimator
Burg estimator 1-72
Capon’s ML estimator 1-72
MVD estimator 1-72
Prony’s method 2-56
Q
QPC 1-88
detection 2-71
synthetics 2-70
qpc.mat 1-137
qpcgen 2-70
qpctor 2-71
q-slice method 1-33
quadratic phase coupling 1-84
quick help 2-55
R
random sequence generator 2-76
recursive instrumental variable (RIV) algorithm
1-56
recursive least squares (RLS) algorithm 1-56
reflection coefficients 1-49, 1-60
residual time series 1-32Index
I-5
resolution 1-65
RIV
double-lattice form 1-58
transversal form 1-56
RIV algorithm 1-56
riv.mat 1-137
rivdl 2-72
rivtr 2-74
RLS algorithm 1-47
rpiid 2-76
S
self-driving AR model 1-66
signal subspace 1-68
skewness 1-7
speech signals 1-122
sunspot data 1-108
synthetic generator
harmonics in noise 2-53
synthetics 1-65
system identification
non-parametric 2-19, 2-21, 2-63
T
TDE
cross-bispectral method 2-80
cross-correlation method 1-101
cross-cumulant method 1-101, 2-77
ML window cross-correlation method 2-82
synthetics 2-81
using hologram 1-105
tde 2-77
tde1.mat 1-137
tdeb 2-79
tdegen 2-81
tder 2-82
TFD’s
Cohen class 1-89
time-delay estimation problem 1-101
time-frequency distribution 1-89
tls 2-84
total least squares 2-84
tprony.mat 1-137
transient signals 1-89
transients modeling 2-56
trench 2-85
Trench recursion 1-49
trench recursion 2-85
tricks 1-131
trispect 2-86
trispectrum 1-8
theoretical 2-86
Wigner 2-94, 2-96
V
variance 1-65
Volterra
non-Gaussian inputs 1-82
Volterra models
arbitrary inputs 2-65
computing output 2-64
Gaussian inputs 2-67
Volterra system 1-80
W
wig2 2-87
wig2c 2-88
wig3 2-90
wig3c 2-92
wig4 2-94Index
I-6
wig4c 2-96
wigdat.mat 1-137
Wigner bispectrum 1-94, 2-90
smoothed 2-92
Wigner cross spectrum 1-90
Wigner spectrum 1-90, 2-87
smoothed 2-88
Wigner trispectrum 1-98, 2-94
sliced 1-98
smoothed 2-96
Wigner-Ville distribution 1-89
window function 1-16, 1-90
Wold’s decomposition 1-5

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