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 deviation .
(a) If the quantizer range is required to
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 distribution function to write an expression for the
p
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 distribution function to write an expression for the
p
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
zeros means and the same variances, how would you generate
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 distribution function to write an expression for the
p
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(t) = Am cos(m t).
(3)
(a) Compute the output SNR in te
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(t), as shown in the
following gure.
Show that Y (t1 )
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 volts. Assume an additive
white Gaussian noise channel w
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
2. Using the Huffman coding procedure, construct a codi
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.
(a) Write down the generator matrix and parity-check m
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 hours
There are THREE questions on this paper.
Answer