INDEX
Ex, 80
F(s)=L[f(t)], 169
Fs, 437
F()=F[f(t)], 305, 344–346
F()=F[f[n]], 587
F(z)+Z[f[n]], 512, 523
H(s)=L[y(t)]/L[x(t)], 197
N, 77
Px, 85
Ts, 456
Xk, 256
1 , 441
0 = 2 π/T 0 , 256
, 656
s, 423
δ(t), 89
δTs(t), 423
ω, 423
τ, 73
x, 458
(nTs), 442
ej`^0 t, 247
h(t), 149
n, 452
r(t), 90
u(t), 89
x[n], 452, 454
xe[n], 464, 465
xo[n], 465
xe(t), 76
xo(t), 76
yzi(t), 130, 215
yzs(t), 130, 215
A
absolutely summable impulse
response, 501, 535–536, 680
absolutely summable signals, 575,
576, 628
advanced signal, 324
amplitude modulation (AM), 87
demodulation, 380
envelope receiver, 381
single sideband, 382–383
suppressed carrier, 379–380
tunable band-pass filter, 379
analog
signal, 9, 67–71
signal, definition, 67
analog communication systems, 730
analog control systems, 363
actuator, 366
cruise control system, 367–369
feedback, 363
open-loop and closed-loop,
364–365
positive and negative
feedback, 363
proportional controller, 366
proportional plus integral (PI)
controller, 367
stability and stabilization,
369–371
transducer, 366
analog filtering, 390
basics, 390–393
Butterworth low-pass design,
391, 393–396
Chebyshev low-pass design,
396–402
Chebyshev polynomials, 396
eigenfunction property, 390
factorization, 391, 393–394, 399
frequency transformations,
402–404
loss function, 392
low-pass specifications, 392
magnitude and frequency
normalization, 393
magnitude-squared
function, 391
specifications, 391–393analog Fourier series
absolutely uniform convergence,
265–270
coefficients, 247
coefficients from Laplace,
255–265
complex exponential, 245–248
convergence, 265–270
DC component, 251
even and odd signals, 279
fundamental frequency, 246,
253, 256
fundamental period, 246
harmonics, 251
linearity, 282–283
line spectrum, 250, 255
mean-square approximation,
266
Parseval’s theorem, 248–250
product of signals, 284
time and frequency shifting,
270–273
time reversal, 280
trigonometric, 251–255
analog Fourier transform
amplitude modulation, 314
convolution, 327–329
differentiation and integration,
346–350
direct and inverse, 299, 301
duality, 310–313
frequency shifting, 313–314
Laplace ROC, 302, 304
linearity, 304–305
periodic signals, 317–320
shifting in time, 345
spectrum and line spectrum, 318
symmetry, 322–327
analog frequency, 619
analog LTI systems
BIBO stability, 153–156 749