Index 675Dirac(t) function, 30
Direct current (DC) transient analysis
application problems, 208–222
examples of, 138–208
overview of circuits, 104–138
response to, 127–138
Direct equation, 321, 330
Dirichlet’s conditions, 323, 331
Discontinuity, 14, 326
Discrete equivalent transfer function, 586
Discrete fi lter transfer function, 584
Discrete Fourier transform (DFT)
average power, 491–492
convolution, 493–499, 502–503, 534–538
correlation functions, 502–503
discrete sequences, 499–500
evaluation of f(n), 495–496
examples, 515–556
features of, 457, 459
f r e q ue n c i e s, 4 89, 49 9, 5 3 0 – 5 3 4
inverse (IDFT), 468–469, 490
length sequences, 489
periodic functions, 500
power spectrum, 492–493
properties of, 493
relationship with DTFT and ZT, 490
sequences, 499–502
Discrete mapping 584
Discrete sequence
components of, 43, 76
exponential, 16
pulse, 12
ramp, 13
reverse time, 24
sinusoidal, 16
step, 12
time, 17, 457
Discrete shifted impulse function, 9–10
Discrete signals
defi ned, 2–3
time, 9, 44
Discrete spectrum, 327
Discrete-step function, 480–481
Discrete systems
analysis synthesis, 458
application problems, 556–560
block diagram, 463–464
bounded input-bounded output (BIBO)
system, 457, 460
causality, 460, 462–463
complex, 462
components of, 458–459
continuous, 475
convolution, 465–468difference equations, 552–553
input sequence, 459, 543–544
invariance, time- or shift, 460
linearity, 459
linear and time invariant (LTI), 461–463,
467–468, 541–545, 556
memoryless, 464
passive, 460
output sequence, 459, 489
signals, 459
single-input, single-output (SISO) systems,
457–458, 460
stability, 460
transfer function, 458, 475, 548–555
Discrete-time Fourier transform (DTFT)
characteristics of, 457, 459, 468–469
comparison with Fourier transform (FT), 472
continuous functions, 472
convergence, 470, 473
examples, 505–556
frequency domains, 470
length sequences, 489–491
magnitude, 469
periodic function, 470, 472
transfer function, 472–473
transform pairs, 470
Discrete time
signals, 9, 44
transfer function, 472
Discrete transfer function, 588
Discrete unit
parabolic function, 14
step function, 11
Distortion
fi lters and, 563
impact of, 563
process, 338
sources of, 330
types of, 321
Distortionless
time-frequency relation, 337
transmission, 337
Distributional calculus, 10
Distribution functions, 5
Don’t care condition, 595
Down-sampling, 44–45
dstep function, 42E
Edison, Thomas, 102
Effective power, 225
Effective value, 225CRC_47760_Index.indd 675CRC_47760_Index.indd 675 7/18/2008 3:10:50 PM7/18/2008 3:10:50 PM