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| Papoulis A. — The Fourier Integral and Its Applications |
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| Предметный указатель |
Periodic signals 42—47
Periodic signals, autocorrelation 250
Periodic signals, cross-correlation 254
Periodic signals, energy spectrum 49
Periodic signals, power spectrum 250
Periodic signals, spectrum analyzer for 153—160
Phase delay 134
Phase distortion 108—117
Phase distortion, arbitrary 114
Phase distortion, Fourier expansion of 114
Phase distortion, parabolic 164
Phase distortion, polygonal approximation 115
Phase distortion, sine variation of 114
Phase lag 86
Phase modulation 132 165
Phase shift 86
Phase shift from attenuation 206
phase velocity 139
Plane waves 136
Poisson distribution 50 232
Poisson’s sum formula 47
Poisson’s sum formula in sampled data 48
Pollock, H. O. 67
Polynomial approximation 53
Polynomial filter 101
Positive definite functions 225
Positive functions 223
Positive functions, convolution of 226 (see also Central-limit theorem)
Positive real functions 307—311
Positiveness, conditions of 58 225
Power spectrum 246
Power spectrum of periodic signals 250
Power spectrum of pulse train 249
Power spectrum, arbitrary 254
Power spectrum, cross 252
Power spectrum, instantaneous 149
Power, finite 245
Principal value, Cauchy 9
Prolate spheroidal wave functions 67
Pulse distortion 119
Pulse modulation 20
Pulse train 44
Pulse train, autocorrelation of 249
Pulse train, power spectrum of 249
Pulse train, Quadrature filter 132
Pulse train, transform of 21
Pulse, rectangular 18
Pulse, transform of 20
Pulse, triangular 18
Pulse-forming filter 116
Ramp, transform of 42
Rational system functions 117
Rational system functions, RM 195
Rational system functions, XM 196
Rectification 162
Residues, applications 297—302
Residues, calculus of 296
Resistance integral theorem 193
Resistance integral theorem, applications 218 266
Response of a system 81
Riemann — Lebesgue lemma 278
Rise time of filters 96
RMS, duration 62
RMS, minimization 33 63
Root, W. L. 240
Running spectrum 148
Running transform 148
Saddle-point method 302 307
Sampler 162
Sampling theorem, frequency 52
Sampling theorem, time 50
Scaling 14
Schwartz, M. 127
| Schwarz’s inequality 63
Schwarz’s lemma 287
Shannon, C. E. 50
Shifting, frequency 15
Shifting, time 14
Signal-front delay 134 187
Signal-front velocity 139
Sine integral 18
Singularity functions, transforms of 36—42 (see also Delta function)
Slepian, D. 67
Smoothing 32
Solodovnikov, V. V. 89
Spectrum analyzer 144—160
Spectrum analyzer for periodic signals 153—160
Spectrum analyzer, error correction 152
Spectrum analyzer, sequential 150—152
Spectrum analyzer, simultaneous 145—150
Spectrum analyzer, steady-state 153—157
Spectrum analyzer, transients 157—160
Spectrum, cross 28 244
Spectrum, energy 28
Spectrum, Fourier 7
Spectrum, power (see Power spectrum)
Spectrum, running 148
Stability 84
Stationary phase, method of 139— 143
Step function, transform of 38
Step modulation, response to 88
Step modulation, transform of 41
Step response 87
Step response, evaluation of 89—92
Step response, overshoot of 90
Stirling’s formula 304
Symmetrical filters 120—131
Symmetry 14
Systems function 86
Thermal noise 266
Time invariance 83
Time-limited signals, duration of 66
Time-limited signals, optimal 70
Time-limited signals, sampling theorem 52
Titchmarsh, E. C. 7
Transformation, low-pass bandpass 122 127
Transformation, system equivalence of 82
Transmission lines 138
Truncated signals 28
Truncated signals, numerical evaluation of 55
Truncated signals, transform of 28
Truxal, J. G. 48
Tukey, J. W. 145
Uncertainty principle 63
Uncertainty principle, band-limited 67
Uncertainty principle, generalization of 67—74
Uncertainty principle, signals, arbitrary 70
Uncertainty principle, time-limited 70
Uncorrelated numbers 254
Unsymmetrical filters 131—134
Uspensky, J. V. 227
Van der Pol, B. 187
Velocity, group 139
Velocity, phase 139
Velocity, signal-front 139
Watson, G. N. 293
Weber, E. 138
Whittaker, E. T. 293
Widder, D. V. 302
Wiener equation 262
Wiener numbers 258 (see also Paley-Wiener condition)
Wiener — Lee transforms 201 209
Wiener, N. 240 258
Wunsch, G. 164
Youla, D. C. 74
Zemanian, A. H. 161
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