高级通信原理习题(含解答)

高级通信原理复习题

Chapter 2

2-1 One experiment has four mutually exclusive outcomes ,1,2,3,4i A i =, and a second experiment has three mutually exclusive outcomes ,1,2,3j B j =. The joint probabilities (,)i j P A B are

111213212223313233414243(,)0.10,(,)0.08,(,)0.13

(,)0.05,(,)0.03,(,)0.09

(,)0.05,(,)0.12,(,)0.14

(,)0.11,(,)0.04,(,)0.06

P A B P A B P A B P A B P A B P A B P A B P A B P A B P A B P A B P A B ===

=========

Determine the probabilities (),1,2,3,4i P A i =, and (),1,2,3J P B i =

2-19 Determine the mean, the autocorrelation sequence and the power density spectrum of the output of a system with unit sample response

1(0)2(1)()1(2)

0()

n n h n n otherwise = −= = = when the input x(n) is a white-no/se process with variance 2

N δ.

Chapter 4

4-11 Consider the four waveforms shown in Fig. P4-11.

a Determine the dimensionality of the waveforms and a set of basis functions.

b Use the basis functions to represent the four waveforms by vectors 1234,,,s s s s ..,

c Determine the minimum distance bclween any pair of vectors.

4-12 Determine a set of orthonormal functions for the four signals shown in Fig.P4-12.

4-18 Determine the signal space representation of the four signals()

k

s t, k = 1, 2, 3, 4 shown in Fig. P4-18 by

using as basis functions the orthonormal function

1()

f t and

2()

f t. Plot the signal space diagram and show that this signal set is equivalent to that for a four-phase PSK signal.

4-20 A PAM partial response signal (PRS) is generated as shown in Fig. P4-20 by exciting an ideal lowpass filter of bandwidth W by the sequence

1n n n B I I −=

+

at a rate 1/2T W =symbols/s. The sequence {}n I consists of binary digits selected independently from the alphabet {1 -1} with equal probability. Hence the filtered signal has the form

1()

(),2n n v t B g t nT T W

∞=−∞=−=

∑ a Sketch the signal space diagram for ()v t ) and determine the probability of occurrence of each

symbol.

b Determine the autocorrelation and power density spectrum of the three-level

c The signal points of the sequence {}n B form a Markov chain. Sketch this Markov chain an

d indicat

e the

transition probabilities among the state.

4-21 The lowpass equivalent representation of a PAM signal is

()

()n n v t I g t nT ∞=−∞=

−∑

Suppose g(t) is a rectangular pulse: and 2n

n n I a a −=

− where {}n a is a sequence of uncorrelated binary-valued (l, -l) random variables that occur with equal

probability. a Determine the autocorrelation function of the sequence {}n I

b Determine the power density spectrum of ()u t

c Repeat (b) if he possible values n a

are (0,1).