Problem Sheet 4
Quantization and baseband transmission
1. A PCM output is produced by a uniform quantizer that has 2n levels. Assume that the input
signal is a zero-mean Gaussian process with standard
Problem Sheet 1
Probability, random processes, and noise
1. If FX (x) is the distribution function of a random variable X and x1 x2 , show that
FX (x1 ) FX (x2 ).
2. Use the denition of the cumulative
Problem Sheet 1
Probability, random processes, and noise
1. If FX (x) is the distribution function of a random variable X and x1 x2 , show that
FX (x1 ) FX (x2 ).
2. Use the denition of the cumulative
E XAM Q UESTIONS
1.
This question is compulsory.
a)
Answer the following questions about probability and random processes.
i)
ii)
Given two statistically independent Gaussian random variables with
zer
Problem Sheet 1
Probability, random processes, and noise
1. If FX (x) is the distribution function of a random variable X and x1 x2 , show that
FX (x1 ) FX (x2 ).
2. Use the denition of the cumulative
Problem Sheet 3
Effects of noise on FM
1. Given the baseband signal-to-noise ratio SN RBaseband , consider an FM detector for singletone modulation, that is, the modulating wave is a sinusoidal wave
m
Problem Sheet 2
Effects of noise on AM
1. A stationary zero-mean Gaussian random process X(t) is passed through two linear lters
with impulse response h1 (t) and h2 (t), yielding processes Y (t) and Z
Problem Sheet 5
Digital modulation and demodulation
1.
(a) Consider a binary ASK modulated-carrier system, which employs coherent demodulation. Let the carrier amplitude at the detector input be 0.7 v
Problem Sheet 6
Information theory
1. By what fraction is it theoretically possible to compress a binary bit stream if the probability
of occurrence of one of the symbols is:
(a) 0.5
(b) 0.2
(c) 0.01
Problem Sheet 7
Coding
1. Repetition codes represent the simplest type of linear block codes. In particular, a single
message bit is encoded into a block of n identical bits, producing an (n, 1) code.
EE2-4
IMPERIAL COLLEGE LON DON
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
EXAMINATIONS 2011
EEEIISE PART II: MEng, BEng and ACGI
COMMUNICATIONS 2
Wednesday, 15 June 2:00 pm
Time allowed: 2:00