Answers to Problems in Random Data

CHAPTER 1

1.1 Period = 2π

1.2 (a) and (c) are periodic; (b) and (d) are nonperiodic

1.3 The autocorrelation function Inline-Equation as τ → ∞

1.4 Variance = 0.09

1.5 Inline-Equation

1.6 (d) is always true

1.7 (c), (d), and (e) are always true

1.8 (a) or (b)

1.9 (b) and (c)

1.10 Only (b) now applies

CHAPTER 2

2.1 f (x) = x|x|

f (x1 + x2) = (x1 + x2)|x1 + x2| ≠ x1|x1| + x2|x2|;

f (cx) = cx|cx| ≠ cx|x|

2.2 f (c1x1 + c2x2) = c1f (x1)+c2f (x2)

2.3 (a) and (b)

2.4 Inline-Equation

2.5 (a) Inline-Equation

(b) Inline-Equation

(c) Inline-Equation

(d) Inline-Equation

2.6 For τ < 0, h(τ) = 0; for τ ≥ 0,

Equation

2.7 From Equation (2.24),

Equation

The maximum response occurs where

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