Random Data: Analysis and Measurement Procedures, Fourth Edition

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 as τ → ∞

1.4 Variance = 0.09

1.5

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

2.5 (a)

(b)

(c)

(d)

2.6 For τ < 0, h(τ) = 0; for τ ≥ 0,

2.7 From Equation (2.24),

The maximum response occurs where

This requires ...