750 Index
analog LTI systems (continued)
causality, 143–145
complete response, 216
continuous-time, 119
convolution integral, 136–143
eigenfunction property, 167,
240, 273
frequency response, 240, 327
impulse response, 138
impulse response, transfer
function, and frequency
response, 329
represented by differential
equations, 214–221
steady-state response, 214
transfer function, 213
transient response, 214
unit-step response, 218, 219
zero-input response, 133, 214
zero-state response, 133, 214
analog systems
causality, 143–145
DC source, 329
passivity, 154
stability, 153
windowing, 331
analog-to-digital converter (ADC),
68, 420
anti-aliasing filter, 430
application-specific integrated
circuit (ASIC), 5
approximate solution of differential
equations, 559B
band-limited signal, 423
basic analog signals
ramp, 90–92
triangular pulse, 90
unit-impulse, 88
unit-step, 89
basic discrete-time signals, 465–478
complex exponentials, 596
damped sinusoid, 466
discrete sinusoids, 469–471
basic signal operations
adder, 72
advancing and delaying, 73
constant multiplier, 71
modulation, 72
reflection, 72
time scaling, 71
windowing, 71
BIBO stability of discrete
systems, 501bilinear transformation, 654–656
warping, 656
block diagrams, 148, 150
bounded-input bounded-output
(BIBO) stability, 153–156,
499–501C
causal
sinusoid, 82, 110
causality
discrete LTI systems, 498
discrete signal, 497–498
discrete systems, 497–500
causal systems and signals, 507–508
channel noise, 379
circular shifting, 607–609
cognitive radio, 6–8
compact-disc (CD) player, 5–6
complex variable function, 23–24
complex variables, 20, 23–24
computer-control systems, 8–9
connection ofs-plane and
z-plane, 513
continuous-time
signal, 67–85
convolution integral, 136–133
commutative property, 148
distributive property, 149
Fourier, 327
graphical computation, 145–147
Laplace, 221
convolution sum, 487–494,
526–537
commutative property, 148
deconvolution, 229
noncausal signals, 533D
delayed signal, 73
difference equations, 18–19,
550–561
digital communications, 709
orthogonal frequency-division
multiplexing (OFDM), 710
PCM, 710
spread spectrum, 710
time-division multiplexing, 730
digital signal processing, 710–722
FFT, 711–715
FFT algorithm, 711
digital signal processor (DSP), 5
digital-to-analog converter, 5,
68, 420discrete complex exponentials,
466–469
discrete filtering
analog signals, 640
bilinear transformation, 640
Butterworth LPF, 658–664
Chebyshev LPF, 666–672
direct, cascade, and parallel IIR
realizations, 698
eigenfunction, 639
FIR design, 681
FIR realizations, 699–700
FIR window design, 681
frequency scales, 652–653
frequency-selective filters, 641
frequency specifications, 659
group delay, 643
IIR and FIR, 643–647
IIR design, 672
linear phase, 641–643
loss function, 648–650
rational frequency
transformations, 672–676
realization, 689–700
time specifications, 652–653
windows for FIR design,
681–683
discrete filters
FIR, 643–647
IIR, 643–647
discrete Fourier series, 599–601
circular representation, 598–599
circular shifting, 607–609
complex exponential, 599–601
periodic convolution, 609–614
Z-transform, 601–602
discrete Fourier transform (DFT),
614–627
fast Fourier transform (FFT), 614
linear and circular
convolution, 624
discrete frequency, 454, 471
discrete LTI systems
causality, 498
response to periodic signals,
273–278
discrete sinusoid, 444
discrete systems
autoregressive (AR), 482
autoregressive moving average
(ARMA), 484
BIBO stability, 500–501
causality and stability, 497–501
convolution sum, 487–494
difference equation
representation, 486–487