Digital Signal Processing
Fifth Edition
Chapter 2
Discrete-Time Signals
and Systems
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Figure 2.1.1 Graphical representation of a discrete-time signal.
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Figure 2.1.2 Graphical representation of the unit sample signal.
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Figure 2.1.3 Graphical representation of the unit step signal.
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Figure 2.1.4 Graphical representation of the unit ramp signal.
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Figure 2.1.5 Graphical representation of exponential signal.
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Figure 2.1.6 Graph of the real and imaginary components of a complex-valued
exponential signal.
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Figure 2.1.7 Graph of amplitude and phase function of a complex-valued
exponential signal: (a) graph of A(n) = rn, r = 0.9; (b) graph of (n) = (/10)n,
modulo 2 plotted in the range (−, ].
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Figure 2.1.8 Example of even (a) and odd (b) signals.
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Figure 2.1.9 Graphical representation of a signal, and its delayed and
advanced versions.
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Figure 2.1.10 Graphical illustration of the folding and shifting operations.
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Figure 2.1.11 Graphical illustration of down-sampling operation.
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Figure 2.2.1 Block diagram representation of a discrete-time system.
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Figure 2.2.2 Graphical representation of an adder.
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Figure 2.2.3 Graphical representation of a constant multiplier.
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Figure 2.2.4 Graphical representation of a signal multiplier.
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Figure 2.2.5 Graphical representation of the unit delay element.
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Figure 2.2.6 Graphical representation of the unit advance element.
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Figure 2.2.7 Block diagram realizations of the system y(n) = 0.25y(n − 1) +
0.5x(n) + 0.5x(n − 1).
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Figure 2.2.8 Examples of a time-invariant (a) and some time-variant systems
(b)–(d).
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Figure 2.2.9 Graphical representation of the superposition principle. T is linear
if and only if y(n) = y(n).
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Figure 2.2.10 Cascade (a) and parallel (b) interconnections of systems.
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Figure 2.3.1 Multiplication of a signal x(n) with a shifted unit sample sequence.
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Figure 2.3.2 Graphical computation of convolution.
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Figure 2.3.3 Graphical computation of convolution in Example 2.3.3.
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Figure 2.3.4 Interpretation of the commutative property of convolution.
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Figure 2.3.5 Implications of the associative (a) and the associative and
commutative (b) properties of convolution.
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Figure 2.3.6 Interpretation of the distributive property of convolution: two LTI
systems connected in parallel can be replaced by a single system with
h(n) = h1(n) + h2(n).
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Figure 2.4.1 Realization of a recursive cumulative averaging system.
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Figure 2.4.2 Realization of the square-root system.
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Figure 2.4.3 Basic form for a casual and realizable (a) nonrecursive and (b)
recursive system.
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Figure 2.4.4 Block diagram realization of a simple recursive system.
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Figure 2.4.5 Illustration of the transient and steady-state response of a first-
order recursive system with a = 0.8 (top) and a = −0.8 (bottom).
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Figure 2.4.6 The weekly Dow Jones Industrial Average index, an SMA
smoothed version with M = 31, and a MA smoothed version with M = 31.
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Figure 2.4.7 The DJIA and an exponentially smoothed version with = 0.1.
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Figure 2.5.1 Steps in converting from the direct form I realization in (a) to the
direct form II realization in (c).
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Figure 2.5.2 Direct form I structure of the system described by (2.5.6).
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Figure 2.5.3 Direct form II structure of the system described by (2.5.6).
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Figure 2.5.4 Structures for the realization of second-order systems: (a)
general second-order system; (b) FIR system; (c) “purely recursive system.”
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Figure 2.5.5 Nonrecursive realization of an FIR moving average system.
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Figure 2.5.6 Recursive realization of an FIR moving average system.
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Figure 2.6.1 Radar target detection.
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Figure 2.6.2 Computation of the autocorrelation of the signal x(n) = an,
0 < a < 1.
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Figure 2.6.3 Identification of periodicity in the Wölfer sunspot numbers: (a)
annual Wölfer sunspot numbers; (b) normalized autocorrelation sequence.
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Figure 2.6.4 Use of autocorrelation to detect the presence of a periodic
signal corrupted by noise.
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Figure P2.2
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Figure P2.49
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Figure CP2.15
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Copyright
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