Signals and Systems - Electrical Engineering

752 Index

power, 79–85, 248–250

average, 80

discrete-time signals, 458–461

instantaneous, 79, 80

proper rational functions, 198–200,

202, 205, 544, 546

pulse amplitude modulation (PAM),

420–421

pulse code modulation (PCM), 729,

730–733

Q

quantization error, 441

quantization step, 441

R

rational functions, 542

real-time processing, 118

S

sampled analog signals, 451

sampled data and digital control,

722–729

closed-loop control, 726–729

feedback, 726

open-loop control, 724–726

sampler time-varying system, 422

sampling

anti-aliasing filter, 430

frequency aliasing, 424

holder for DAC, 439

Nyquist rate, 431

Nyquist-Shannon theorem,

437–439

Parseval’s application, 427

period, 431

practical aspects, 420, 439–446

quantization, 439

quantization and coding, 68

quantization error, 441, 442

quantizer, 441

rate, 430

sample-and-hold system, 440

sampling period, 69

signal recovery, 429

sinc interpolation, 432–433

sampling frequency, 423

sampling function, 421

sampling period, 431

sampling rate, 430

Shannon, 430

sifting property ofδ(t), 106

signal radiation with antenna, 317

signal recovery in sampling, 429

signals

absolutely integrable, 81

absolutely summable, 575, 576,

628

advanced, 74

analog, 68

aperiodic, 66, 77–79

band-limited, 423

basic analog signals, 85–106

causal, anti-causal, noncausal,

174

causal discrete sinusoid, 454

causality, 145

causal sinusoid, 82

complex exponentials, 87

continuous-time, 67–85

convolution integral, 141

delayed, 73

deterministic, 66

digital, 67

discrete finite energy, 459

discrete periodic sinusoids, 454

discrete sinusoid, 444

discrete time, 67

even, 66, 75–77

even and odd decomposition,

75, 76

finite energy, 66, 80

finite-energy discrete signal,

458–461

finite power, 79–85

finite support, 71

full-wave rectified, 99, 262

inherently discrete, 452

modulation, 126

odd, 66, 75–77

periodic, 66, 77–79

piecewise smooth, 266

random, 65

real and imaginary parts, 86

sampled analog, 470

shifting and reflecting, 74

sinc, 311

sinusoids, 70, 87

smooth, 266

speech, 69

square integrable, 80

square summable, 458

train of rectangular pulses, 143

windowing, 72

sinc interpolation of recovered

signals, 433

sinusoidal steady-state phasor,

24–26

software-defined radio, 6–8

spectrum analyzer, 248

square summable signals, 458.See

alsoFinite-energy

discrete-time signals

stability, discrete systems, 478

system

all-pass, 243

amplitude modulation (AM),

126

analog, 119

analog averager, 158

averager, 158

communications, 383

continuous-time, 120

definition, 117

differential equation

representation, 131

digital, 119

discrete-time, 119

hybrid, 119

ideal communication system,

243

linearity, 120

multipath channel, 170

nonlinear, 127

RLC circuit, 129–130

time-invariance, 118

time-varying, 128

vocal system, 128

T

trapezoidal rule approximation, 19,

654, 655

transient analysis, 371

U

uniform sampling, 420–437

Z

Z-transform

connection with sampling,

601–602

damping radius, 511

discrete frequency, 511, 523

inverse, 511, 527, 542,

543–550, 562

linearity, 522–524, 541, 555, 557

one-sided transform, 515,

521–537, 542–550

ROC and uniqueness, 516–521

for sampled signals, 512

significance of poles, 511

solution of difference equations,

550–561

time-shifting, 533, 555, 557

two-sided transform, 515–521,

561–564