Index
0-9 and, Symbols
Ex
80
Fs
437
N
77Px
85Ts
456Xk
256Δ
441Ω0 = 2π/T0
256Ω
656Ωs
423δ(t)
89δTs(t)
423ω
423τ
73ϵx
458ϵ(nTs)
442ejℓΩ0t
247h(t)
149n
452r(t)
90u(t)
89xo[n]
465xe(t)
76xo(t)
76A
advanced signal
324amplitude modulation (AM)
87demodulation
380envelope receiver
381single sideband
382–383suppressed carrier
379–380tunable band-pass filter
379analog communication systems
730analog control systems
363actuator
366cruise control system
367–369feedback
363open-loop and closed-loop
364–365positive and negative feedback
363proportional controller
366proportional plus integral (PI) controller
367stability and stabilization
369–371transducer
366analog filtering
390basics
390–393Chebyshev low-pass design
396–402Chebyshev polynomials
396eigenfunction property
390frequency transformations
402–404loss function
392low-pass specifications
392magnitude and frequency normalization
393magnitude-squared function
391specifications
391–393analog Fourier series
absolutely uniform convergence
265–270coefficients
247coefficients from Laplace
255–265complex exponential
245–248convergence
265–270DC component
251even and odd signals
279fundamental period
246harmonics
251linearity
282–283mean-square approximation
266Parseval's theorem
248–250product of signals
284time and frequency shifting
270–273time reversal
280trigonometric
251–255analog Fourier transform
amplitude modulation
314convolution
327–329differentiation and integration
346–350duality
310–313frequency shifting
313–314linearity
304–305periodic signals
317–320shifting in time
345spectrum and line spectrum
318symmetry
322–327analog frequency
619analog LTI systems
BIBO stability
153–156causality
143–145complete response
216continuous-time
119convolution integral
136–143impulse response
138impulse response, transfer function, and frequency response
329represented by differential equations
214–221steady-state response
214transfer function
213transient response
214anti-aliasing filter
430application-specific integrated circuit (ASIC)
5approximate solution of differential equations
559B
band-limited signal
423basic discrete-time signals
465–478complex exponentials
596damped sinusoid
466discrete sinusoids
469–471basic signal operations
adder
72advancing and delaying
73constant multiplier
71modulation
72reflection
72time scaling
71windowing
71BIBO stability of discrete systems
501C
causal systems and signals
507–508channel noise
379circular shifting
607–609cognitive radio
6–8compact-disc (CD) player
5–6complex variable function
23–24computer-control systems
8–9connection of s-plane and z-plane
513continuous-time
signal
67–85D
delayed signal
73digital communications
709orthogonal frequency-division multiplexing (OFDM)
710PCM
710spread spectrum
710time-division multiplexing
730digital signal processor (DSP)
5discrete complex exponentials
466–469discrete filtering
analog signals
640bilinear transformation
640Butterworth LPF
658–664Chebyshev LPF
666–672direct, cascade, and parallel IIR realizations
698eigenfunction
639FIR design
681FIR realizations
699–700FIR window design
681frequency scales
652–653frequency-selective filters
641frequency specifications
659group delay
643IIR and FIR
643–647IIR design
672linear phase
641–643loss function
648–650rational frequency transformations
672–676realization
689–700time specifications
652–653windows for FIR design
681–683discrete Fourier series
599–601circular representation
598–599circular shifting
607–609complex exponential
599–601periodic convolution
609–614Z-transform
601–602discrete Fourier transform (DFT)
614–627fast Fourier transform (FFT)
614linear and circular convolution
624discrete sinusoid
444discrete systems
autoregressive (AR)
482autoregressive moving average (ARMA)
484BIBO stability
500–501causality and stability
497–501convolution sum
487–494difference equation representation
486–487moving average (MA)
481–482nonlinear system
498time-invariance
498discrete-time Fourier transform (DTFT)
572–596convergence
591convolution sum
595–596downsampling and upsampling
582eigenfunctions
573–575Parseval's theorem
585–587sampled signal
578–580symmetry
589–595time and frequency shifts
628time-frequency duality
628time-frequency supports
580–585Z-transform
573–575discrete-time signals
basic
465–478definition
452Fibonacci sequence
453finite energy
458–461finite power
458–461inherently discrete-time
452sample index
452sinusoid
469–472square summable
458discrete transfer function
655F
Fibonacci sequence
difference equation
453field-programmable gate array (FPGA)
5Fourier basis
247frequency, harmonically related
83frequency aliasing
424frequency modulation (FM)
87H
hybrid system
119I
ideal impulse sampling
421–428L
Laplace transform
convolution integral
196–197derivative
189integration
193–194linearity
185–188one-sided
176–197proper rational
198two-sided
166–176length of convolution sum
721LTI systems, superposition
135–136M
magnitude line spectrum
249Matlab
analog Butterworth and Chebyshev filter design
414analog Butterworth filtering
414control toolbox
375decimation and interpolation
585DFT and FFT
577discrete filter design
644DTFT computation
577FFT computation
717filter design
405–408Fourier series computation
603–604functions
36general discrete filter design
646numerical computations
30phase computation
591phase unwrapping
592plotting
39–41saving and loading
41–43symbolic computations
43–53vectorial operations
33–35vectors and matrices
30–33N
negative frequencies
323nonlinear filtering, median filter
495nonzero initial conditions
552normality
247Nyquist sampling rate
431Nyquist sampling theorem
431S
sampled analog signals
451sampled data and digital control
722–729closed-loop control
726–729feedback
726open-loop control
724–726sampler time-varying system
422sampling
anti-aliasing filter
430frequency aliasing
424holder for DAC
439Nyquist rate
431Nyquist-Shannon theorem
437–439Parseval's application
427period
431quantization
439quantization and coding
68quantizer
441rate
430sample-and-hold system
440sampling period
69signal recovery
429sinc interpolation
432–433sampling frequency
423sampling function
421sampling period
431sampling rate
430Shannon
430sifting property of δ(t)
106signal radiation with antenna
317signal recovery in sampling
429signals
absolutely integrable
81advanced
74analog
68band-limited
423basic analog signals
85–106causal, anti-causal, noncausal
174causal discrete sinusoid
454causality
145causal sinusoid
82complex exponentials
87continuous-time
67–85convolution integral
141delayed
73deterministic
66digital
67discrete finite energy
459discrete periodic sinusoids
454discrete sinusoid
444discrete time
67finite-energy discrete signal
458–461finite power
79–85finite support
71inherently discrete
452modulation
126piecewise smooth
266random
65real and imaginary parts
86sampled analog
470shifting and reflecting
74sinc
311smooth
266speech
69square integrable
80square summable
458train of rectangular pulses
143windowing
72sinc interpolation of recovered signals
433sinusoidal steady-state phasor
24–26software-defined radio
6–8spectrum analyzer
248square summable signals
458stability, discrete systems
478system
all-pass
243amplitude modulation (AM)
126analog
119analog averager
158averager
158communications
383continuous-time
120definition
117differential equation representation
131digital
119discrete-time
119hybrid
119ideal communication system
243linearity
120multipath channel
170nonlinear
127RLC circuit
129–130time-invariance
118time-varying
128vocal system
128U
uniform sampling
420–437..................Content has been hidden....................
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