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Bibliography
Abramowitz, M., and I. Stegun (1965), Handbook of Mathematical Functions, Dover, New York. Anderson, Brian D.O., and John B. Moore (1979), Optimal Filtering, Prentice-Hall, Englewood
Cliffs, N. J. Asefi, T. (1978), Stochastic Process, Estimation Theory and Image Enhancement, JPL Publication,
Pasedena, Calif. Astrom, Karl J. (1970), Introduction to Stochastic Control Theory, Academic, New York. Balakrishnan, A. V., ed. (1966), Advances in Communication Systems, vol. 2, Academic, New York. ---, ed. (1968), Communication Theory, McGraw-Hili, New York. Bartlett, M. S. (1978), An Introduction to Stochastic Processes, Cambridge Univ. Press, New York. Battin, R. (1964), Astronomical Guidance, McGraw-Hili New York. Bellman, Richard E. (1967), Introduction to Mathematical Theory of Control Processes, Linear
Equations and Quadratic Criteria, vol. 1 Academic, New York. --- (1970), Introduction to Matrix, McGraw-Hili New York. ---, and S. Dryfus (1962), Applied Dynamic Programming, Princeton University Press, Prince-
ton, N.J. ---, and R. E. Kalaba (1965), Quasilinearization and Nonlinear Boundary-Value Problems,
vol. 3 American Elsevier, New York. Bendat, Julius S., and Allan G. Piersol (1971), Random Data: Analysis and Measurement Pro
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Huntington, N.Y. Bendat, Julius S., and A. G. Piersol (1980), Engineering Aspects of Correlation and Spectral
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Calif. Brighham, E. D., and R. R. Morrow (1967), The Fast Fourier Transform, IEEE Spectrum, 63-70. Brogan, W. L. (1974), Modern Control Theory, Quantum Publishers, New York. Brown, R. G. (1983), Introductions to Signal Analysis and Kalman Filtering, Wiley, New York. Bryson, Arthur E., Jr. and Yu-Chi-Ho (1975), Applied Optimal Control Optimization Estimation
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London. Childers, Donald G. ed. (1978), Modern Spectrum Analysis, IEEE Press, selected reprint series. Chung, K. L. (1968), Probability, Harcourt, Brace Jovanovich, New York. Claerbout,1. F. (1976), Fundamentals of Geophysical Data Processing, McGraw-Hili, New York. Conover, W. 1. (1980), Practical Nonparametric Statistics, Wiley, New York.
649
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Alternative hypothesis (see Hypothesis) Amplitude modulated signal, 11 Amplitude shift keying (see ASK) Analytic function, 168 Analytic signal, 51 Antenna gain, 645 Antipodal signal (see Signal) A periodic convolution, 26 A posteriori density, 357 A priori probability, 355, 492 ARMA,321 AR process, 321 ASK, 12 ASN, 578, 586-589 Asymptotically stable, 144-145 Asymptotic relative efficiency, 491, 599 Autocorrelation
coefficient, 31 function, 23,309
Autocovariance,309 Autogressive process, 321 Autoregressive-moving average process, 321 Average sample number, 578, 586-589 Average value, 16,212 (see Mean, Expected
value, First moment) ensemble (see Expected value), 212 statistical (see Mean), 212 time (see Sample mean), 16
143 Bilinear z transform, 71 Binary detection (see Detection) Binary frequency shift keying (see BFSK) Binary hypothesis (see Hypothesis) Binary phase shift keying (see BPSK) Binomial
Curve fitting (see Linear regression) Cyclo-stationary process, 425
Data rate, 644 Decision space, 479 Delta function, 20 De Moivre-Laplace theorem, 276, 596 Demodulation (see Detection) DeMorgan's law, 257 Density function
Discrete matched filter, 401, 439 Discrete Wiener filter, 416-420 Dispersion matrix, 241 Distortionless, 47 Distribution-free tests,S 90 Distribution function (see also Probability
lnphase component, 522 Integrate and dump filter, 404, 622 Interarrival time, 283 Intersection of sets (see Product of sets) Inverse
Fourier transform, 26 Laplace transform, 36
of matrix, 90 z transform, 76, 80
Jacobian, 270 Joint
INDEX 659
characteristic function, 280 distribution, 234, 270 Gaussian density (see Gaussian vector) probability density, 279
Kalman filtering, 453-456 Kalman gain, 456 Karhunen-Loeve expansion, 334,542 Karhunen-Loeve transformation, 337 Kolomogorov equations, 429 Kolomogorov-Smirnov test (see Non-
Parametric) Kronecker
delta function, 65 product, 158
Kruskal-Wallis test (see Nonparametric)
Laplace transform convolution theorem, 37 differentiation, 36 final value theorem, 37 initial value theorem, 36 integral theorem, 37 inverse transform, 36 linearity, 36 time-delay, 36 transform pair's, 35-36
Laplacian random variable, 266, 600 Laurent series expansion, 173 Law of large numbers, 274 Least squares estimator, 374 Levinson-Durbin algorithm, 456 Likelihood
function, 468--469, 494 ratio, 468--469, 494
Limit theorems central limit theorem, 274 Kinchin's theorem, 274 Kolmogorov theorem, 274 large number, 274 Lindberg-Levy, 275
Linear estimation (see Estimator) filter, 45 independence, 104, 105 mean square estimator, 356 minimum variance estimator, 352 phase, 47
660 INDEX
Linear (continued)
prediction (see Prediction filter) regression, 374 system, 45-50
Parzen window, 446 Path loss, 642 PCM,623 PDF (see Density function) Periodic convolution, 67 Periodic process, 424 Periodogram, 428
INDEX 661
Phase shift keying (see BPSK) Physical realizability (see Causal) Point process, 286 Poisson distribution, 220, 301 Poisson process, 288, 301 Polynomial curve filtering (see Curve
fitting) Positive definite, 101, 112 Power
series (see Taylor's) signal, 26
Power spectral density BPSK,625 CPM,626 FSK,626 MSK,625 QAM,626 QPSK,625
Power test, 460 Pre-envelope, 425 Prediction filter, 442, 447-448 Predictor, 442, 453 Pre-whitening filter, 402, 545 Principal part, 174 Pro bability
a priori, 355,492 axioms, 201-202 conditional, 247 density function (see Density function) of detection, 465 of error, 460 of false alarm, 460 of miss, 460 space, 201
Probability distribution function beta, 267 binomial, 267 Cauchy, 267 chi-square, 255 Erlang, 266 exponential, 261 gamma, 266 Laplace, 266 log-normal, 256 Maxwell,267 normal,346 normal-bivariate, 233
662 INDEX
Probability distribution function (continued) poisson, 267 Rayleigh, 266 student's, 255 triangular, 268 uniform, 268
PSD (see Power spectral density) Pseudo-inverse matrix, 109 PSK,571 Pulse Code Modulation (see PCM)
Statistically independent, 249 Steady state, 40 Step function (see Unit step function) Stochastic process (see Random process) Strictly stationary process, 286 Student-t-density,255 Sufficient statistics, 354 Sylvester's theorem, 101 Symbol rate, 568 Symmetric matrix, 85 Symmetry condition, 279 System
cascade, 426 causal, 46 dynamical, 39, l37, 141-142 feed-back, 195,426 impulse response function, 40, 46, 317 line~,46,65, 137, 141-142 time inv~iant, 46, 65 time variant, 46 transfer function, 47, l31
Tapped delay line (see Transversal filter) Taylor's series expansion, 3 Telegraph signal, 423 Temporarily homogeneous, 305 Timing error, 622 t-test (see nonparametric) Three sigma, 220 Threshold level, 460 Tiknov density, 619 Time update, 455 Total probability theorem, 248 Trace of matrix, 158 Transfer function, 46, 131 Transform