Digital Signal Processing (4th Ed) [OCR] ( PDFDrive )_compressed-501-1103-401-603

Index 1081

J Linear prediction filter (see Natural response 95
Linear prediction) Natural signals 267-268
Joint-process estimate 938--940 575 Noise subspace 1017
Noise whitening filter 835
K Linear predictive coding 897 Normal equations 846
of speech 897-900
Kalman gain vector 918 solution of 846--854
LMS algorithm 905-907 Levinson-Durbin algo-
L excess mean-square error of rithm 846-850
908 Schur algorithm 850-853
Lattice filter algorithms properties of 907
927-954 Number representation
Local loop 888 601-608
a posteriori form 940 Low-frequency signal 265
a priori form 940 Lowpass filter 327 fixed-point 601--605
error-feedback form 944 LTI systems 112-116 floating point 605-608
gradient form 950-951 Nyquist rate 28
joint process estimate moving average 113
second order 112-113 o
938--940 structures 108--116
modified form 940-946 One's complement. 603
normalized form 949-950 canonic form 112 One-sided z-transform
properties of 951-954 direct form I 108--109
square-foot form 949-950 direct form II 109-113 205-211
Lattice filters 574--579 nonrecursive 112-116 Orthogonality principle
recursive 112-116
594--601, 858--862, 874 weighted moving average 866-867
ARMA structure 860-862 Oscillators (sinusoidal genera-
AR structures 858--860 112
MA structure 838--841 tors) 347
LDU decomposition 921-923 M CORDIC algorithm for
Leakage 489, 964
Learning curves 911 Maximal ripple filters 685 349
Least squares 746-747 coupled-form 347-349
filter design 746-747 Maximum entropy method digital 347
Least-squares estimation Overflow 629--631
993 Overlap-add method 487-488
907 Overlap-save method 485-487.
Levinson-Durbin algorithm Maximum-phase system Overload noise 407
Oversampling NO 433-440
846-850 354--357 Oversampling D/A 439
generalized 850, 876
split Levinson 874 Mean square estimation 866
Limit cycle oscillations
903-905 '
624--629
Linear filtering 480-488 orthogonality principle

based on DFf 480-488 866-867
overlap-add method
Minimum description length p
487-488
overlap-save method (MDL) 997

485-487 Minimum-phase system Paley-Wiener theorem 656
Linear interpolation 427-440
Linear prediction 578, 354-357 Parseval's relations 238 255

838--858 Minimum variance estimate 287, 479 "
backward 841-845
forward 838-841 1012-1015 aperiodic (energy) signals
lattice filter for 845
normal equations for 846 Mixed-phase system 354--357 238, 255, 287
properties of 855-858
Moving-average filter 304 DFf 479

Moving-average (MA) process periodic (power) signals

837,987 230,246

autocorrelation of 837 Partial energy 358

Moving-average signal 115 Partial fraction expansion (see

Multichannel signal 8 Inverse z-transform)

Multidimensional signal 6-9 Periodogram 966-971

N estimation of 966-971

Narrowband signal 266 mean value 968

variance 968

/'

1082 Index

Phase 12 computational require- of WeIch estimate 982-983
maximum 354-357 ments 984-985 Quantization 20, 31-35,
minimum 354-357
mixed 354-357 performance characteris- 403-406
reSponse 306 tics 981-984 differential 433
differential predictive 434
Pisarenko method 1015-1019 WeIch 975-977,982-983 dynamic range 33, 404, 605
Poles 170 parametric (model-based) error 31, 34, 613-639
in AID conversion 403-406
complex conjugate 189-192, methods 985-1009 in filter coefficients 613-620
204-205 ARMA model 988, level 32, 403
resolution 32, 605
distinct 173-198 999-1001 rounding 32, 608-612
location 173-198 AR model 989 step size 32, 605
multiple-order 187-188 AR model order selection truncation 32, 608-612
Polyphase filters 766-767 Quantization effects 31, 405,
for decimation 768 996-997
for interpolation 773 Burg method 990-994 549, 601
Power 46 least-squares 994-995 fixed-point numbers
definition 46 MA model 990, 997-999
signal 47 maximum entropy method 601-605
Power density spectrum one's complement 603
993 sign-magnitUde 603
229-233 model parameters table of bipolar codes
definition 230
estimation of (see also Power 988-990 406
modified Burg 991 two's complement
spectrum estimation) relation to linear predic-
230 603-605
periodic signals 229-233, tion 988-990 floating-point numbers
245-248 sequential least squares
random signals 828-830 605-608
rectangular pulse train 995-996 in AID conversion 34-35,
232-233 Yule-Walker 990
POwer spectrum estimation USe of D FT 971-973 406-408
963 Prediction coefficients 839 in computation of DFT
Capon (minimum variance) Prediction-error filter 574, 839
method 1012-1015 properties of 855-858 549-555
direct method 963 Principal eigenvalues 1020 direct computation
eigenanalysis algorithms Probability density function
1019-1028 549-551
ESPRIT 1'022-1025 824-825 FFf algorithms 551-555
MUSIC 1021 Probability distribution in filter coefficients 613-620
order selection 1025-1026 limit cycles 624-629
Pisarenko 1015-1019 function 1041-1044 dead band 625
experimental results Prony's method 746-747 overflow 629-631
1001-1009 Pseudorandom sequences zero-input 625
from finite data 966-973 scaling to prevent overflow
indirect method 963 145
leakage 964 Barker sequence 145 629-631
nonparametric methods maximal-length shift register statistical characterization
973-985
Bartlett 974-975 sequences 144-145 631-639
Blackman-Thkey Quantizer 403
977-981, 983-984 Q
midrise 404
Quadrature mirror filters midtread 404
788 resolution 403-405
uniform 404
for perfect reconstruction
798-799 R

for subband coding 788 Random number generators
Quality 981-984 1041-1046

of Bartlett estimate 982
of Blackman-Tukey estimate

983-984

Index 1083

Random processes 323-326, Reflection coefficients 575, of bandpass signals 779-781
824-833 598,845-846,927 polyphase filters for

averages 825-831 Resonator (see Digital 766-767
autocorrelation 826 resonator) Sampling theorem 26-28,
autocovariance 826
expected value 825 Reverse (reciprocal) polyno- 384-394
for discrete-time signals mial 579, 842 Schur algorithm 850-853
829-830
moments 825 backward system function pipelined architecture for
power 826 579,842 853-854

correlation-ergodic 832-833 Round-off error 608-612, split-Schur algorithm 874
discrete-time 829-830 631-639 Shanks'method 748-749
ergodic 830 Sigma-delta modulation 436
jointly stationary 825 s Signal flowgraphs 584-588
mean-ergodic 831-832 Signals 2-4
power density spectrum Sample-and-hold 402-403, 409
Sample function 825 analog 9
828-829 Sampling 9, 19, 21, 384-394 antisymmetric 48
response of linear systems aperiodic 48
aliasing effects 25-26 bandpass 266
323-326 frequency 21 continuous-time 9
autocorrelation 323-326 frequency domain 449-454 deterministic 11
expected value 323 interval 21 digital 10
power density spectrum Nyquist rate 28 discrete-time 9, 36-52
of analog signals 21-31, electrocardiogram (EeG)
324-326
sample function 825 384-394 8
stationary 825 of discrete-time signals harmonically related 17
multichannel 8
wide-sense 826 751-806 multidimensional 9
time-averages 830-832 of sinusoidal signals 22-26 natural 267
Random signals (see Random period 21
periodic 21 frequency ranges 267-268
processes) rate 21 periodic 13
Rational z-transforms 184-193 theorem 26-28 random 11, 824-833
time-domain 22-26,384-394
poles 170-173 uniform 21 correlation-ergodic
zeros 170-173 Sampling-rate conversion 832-833
Recursive least squares
762-806 ergodic 824
907-954 (see also Sampling-rate expected value of 825
direct-form FIR algorithms mean-ergodic 832-833
conversion) moments of 826-830
907-927 applications of 784-806 statistically independent
fast LS 923-925,945-947
properties of 925-927 for DFf filter banks 827
lattice algorithms 928-954 790-796 strict-sense stationary
a posteriori form 940
a priori form 940 for interfacing 785 825
error-feedback form for lowpass filters 786 time-averages 830-833
for phase shifters 784-785 unbiased 831
944 for subband coding uncorrelated 827
gradient 950-951 wide-sense stationary
joint process estimate 787-788
for transmultiplexing 826
938-940 seismic 268
modified form 940-946 796-798 sinusoidal 12
normalized form 949-950 by arbitrary factor 781-782 speech 2-4
properties of 951-954 by rational factor 762-766 symmetric 48
square-root form 921-923 decimation 751-760 Signal subspace 1020
Recursive systems 112-116 filter design for 762-775
interpolation 751,760-762
multistage 775-779

1084 Index

Sign magnitude representation steady-state 195-196 y
603 transient 104, 195-196
zero-input 95 Yule-Walker equations 846
Sinusoidal generators (see zero-state 94 modified 1000
Oscillators)
T Yule-Walker method 990
Spectrum 225-226
analysis 226 Time averages 830-833 z
estimation of 226,961-1028 Time-limited signals 266
(see also Power spectrum Toeplitz matrix 847,864 Zero-input linear 96
estimation) 226 Transient response 104, Zero-input response 95
Zero-order hold 34, 409
Split-radix algorithms 532-536 195-196, 309-311 Zero padding 456
Spread-spectrum signal 892 Transition band 660 Zeros 170
Stability of LTI systems 1Tansposed structures 584-588 Zero-state linear 96
Truncation error 32, 608-612 Zoom frequency analysis
196-203 Trunk lines 888
of second-order systems Two's complement representa- 821-822
z-transforms 147
201-203 tion 603
Stability triangle 202 definition 147-148
Steady-state response u bilateral (two-sided)
147-148
195-196, 311-312 Uniform distribution 407, unilateral (one-sided)
Structures 108-116 549-551, 608-612 205-211

direct form I 108-109 Unit circle 261-265 inverse 156-170, 179-193
direct form II 109-113 Unit sample (impulse) by contour integration
Subband coding 787-789 156-157, 180-182
Superposition principle 63 response 106-108 by partial
Superposition summation Unit sample sequence 43 fraction-expansion
184-193
73 v by power series 182-184
System 3, 53-56
Variability 981 properties 157-170
dynamic 60 Variance 549-551,631-639 convolution 164-166
finite memory 60 correlation 166-167
infinite memory 60 w differentiation 163-164
inverse 350 initial value theorem
invertible 350 Welch method 975-977, 168
relaxed 56 982-985 linearity 157-159
System function 177-179, multiplication 167-168
Wideband signal 266 Parseval's relation 168
314-317 Wiener filters 862-873, 904 scaling 161-162
of all-pole system 179 table of 169
of all-zero system 177-179 FIR structure 864-866 time reversal 162
of LTI systems 177-179 for filtering 863 time shifting 159-161
relation to frequency for prediction 863
for smoothing 863 rational 170-179
response 314-317 IIR structure 867-871 region of convergence
System identification 350, noncausal 871-873
Wiener-Hopf equation 864 (ROC) 147-156
358-360 Wiener-Khintchine theorem relationship of Fourier
System modeling 836
System responses 94 285 transform 259-261
Window functions 668 table of 169
forced 95 Wold representation 836
impulse 106-108 Wolfer sunspot numbers 10
natural (free) 95,212
of relaxed pole-zero systems autocorrelation 125

170-179
of systems with initial

conditions 211-214