Signals and Systems - Electrical Engineering

Index 751

moving average (MA), 481–482
nonlinear system, 498
time-invariance, 498
discrete-time Fourier transform
(DTFT), 572–596
convergence, 591
convolution sum, 595–596
downsampling and
upsampling, 582
eigenfunctions, 573–575
Parseval’s theorem, 585–587
sampled signal, 578–580
symmetry, 589–595
time and frequency shifts, 628
time-frequency duality, 628
time-frequency supports,
580–585
Z-transform, 573–575
discrete-time signals
absolutely summable, 575,
576, 628
basic, 465–478
definition, 452
Fibonacci sequence, 453
finite energy, 458–461
finite power, 458–461
inherently discrete-time, 452
sample index, 452
sinusoid, 469–472
square summable, 458
discrete transfer function, 655

E
energy, 80
discrete-time signals, 458–461
Euler’s identity, 23–24, 87
even signal, 279, 461–465

F
Fibonacci sequence
difference equation, 453
field-programmable gate array
(FPGA), 5
filtering, 276–278, 327–344
analog, 390–408
median filter, 495
filters
anti-aliasing, 430
passband, 332
RC high-pass filter, 336
RC low-pass filter, 277
finite calculus, 9
finite difference, 12–13
summations, 13–16

FIR filters and convolution sum,

528, 529, 531, 533

Fourier basis, 247

four-level quantizer, 441, 442

frequency, harmonically related, 83

frequency aliasing, 424

frequency modulation (FM), 87

frequency response, poles and zeros,

342, 343

G

Gibb’s phenomenon, 266, 267

filtering, 334

graphical convolution sum, 530

H

hybrid system, 119

I

ideal filters

band-pass, 332

high-pass, 332

linear phase, 332

low-pass, 332

zero-phase, 333

ideal impulse sampling, 421–428

inverse Laplace

with exponentials, 209

partial fraction expansion, 198

two-sided, 212–214

inverse Z-transform, 542–563

inspection, 542

long-division method, 542–543

partial fraction expansion,

544–546

positive powers of z, 545, 546

L

Laplace transform

convolution integral, 196–197

derivative, 189

integration, 193–194

inverse, 169, 197–214

linearity, 185–188

one-sided, 176–197

proper rational, 198

region of convergence (ROC),

166, 172–176

transfer function, 214, 223

two-sided, 166–176

length of convolution sum, 721

L’Hopital’s rule, 101, 306, 433

LTI systems, superposition, 135–136

M

magnitude line spectrum, 249

Matlab

analog Butterworth and

Chebyshev filter design, 414

analog Butterworth filtering, 414

control toolbox, 375

decimation and interpolation,

585

DFT and FFT, 577

discrete filter design, 644

DTFT computation, 577

FFT computation, 717

filter design, 405–408

Fourier series computation,

603–604

functions, 36

general discrete filter design, 646

numerical computations, 30

phase computation, 591

phase unwrapping, 592

plotting, 39–41

saving and loading, 41–43

symbolic computations, 43–53

vectorial operations, 33–35

vectors and matrices, 30–33

N

negative frequencies, 323

nonlinear filtering, median

filter, 495

nonzero initial conditions, 552

normality, 247

Nyquist sampling rate, 431

Nyquist sampling theorem, 431

O

odd signal, 75–77

one-sided Z-transform, 511

orthogonality, 248

P

Parseval’s relation and sampling,

427

periodic convolution, 609–614, 624

periodic discrete sinusoids, 454, 456

phase line spectrum, 249, 250, 253,

257, 259, 261, 263, 265

phase modulation (PM), 87, 378,

386

phasors, sinusoidal steady state,

24–26, 28

poles and zeros, 172–176

poles and zeros of Z-transforms, 511,

549, 551, 564