Introduction to Random Signals and Noise

Index

Symbols

δ-function, 5, 67, 78, 81, 83, 205, 242

discrete-time -, 82

δ-pulse, 51

a.c. component, 27

aliasing, 86

distortion, 52

amplifier

front-end -, 146

low-noise -, 146

optical -, 145

amplitude modulated (AM) signal, 101

amplitude shift keying (ASK), 112, 173, 190

analog-to-digital conversion, 54

analytic

function, 180, 181

signal, 102

antenna noise, 144

anti-causal function, 180, 181

antipodal signals, 222

attenuation, 229

autocorrelation function, 11, 69

properties of -, 13

autocorrelation of discrete-time process, 32, 57, 90

autocovariance of discrete-time process, 32

available

power gain, 138

spectral density, 134

spectral density in amplifiers, 138

average

time -, 14

band-limited process

definition of -, 74

band-limiting filter

definition of -, 74

bandpass

filter, 73

signal, 101

bandpass filtering

of white noise, 110

bandpass process, 44

conversion to baseband, 119

definition of -, 74

direct sampling of -, 119

properties of -, 107

bandwidth

of bandpass process, 44

of low pass process, 43

root-mean-squared (r.m.s.) -, 43

baseband process

definition of -, 74

Bayes' theorem, 155

Bessel function, 113

biorthogonal signals, 225

binary detection

in Gaussian noise, 158

binary phase shift keying (BPSK), 191

bipolar nonreturn-to-zero (NRZ) signal, 98

bit error probability, 155, 157

Boltzmann's constant, 130, 247

Brownian motion, 130, 133

Butterworth filter, 98

Campbell's theorem, 201

extension of -, 204, 206

CATV networks, 225

causality, 68

chain rule, 232

characteristic frequency, ...