Random Variables
(Supplementary materials)
Transformation of Random Variables
Given a random variable X, which is characterized by its pdf p(x), we
sometimes need to determine the pdf of the random variable Y=g(X),
where g(X) is some given function of X.
Fourier Series and Transform
Fourier Series
Given a signal x(t) defined over the interval (t0, t0+T0) with the
definition
2
T0
0 = 2f 0 =
We define the complex exponential Fourier series as
x(t ) =
X
n =
n
e jn0t
t0 t t0+T0
where
1
Xn =
T
t 0 +T0
t0
x(t
Chapter 4
Optimum Receiver Principles
Outline
1. Matched Filter
2. Decision Theory
3. Maximum a posteriori (MAP) Detection
4. Error Probability Analysis
2/56
Demodulation and Detection of
Digital Signals
(t)
si(t)
Channel
hc(t)
si(t)hc(t)
t=T
Freq.
Down
C
Chapter 2
Review of
Mathematical Preliminaries
Outline
1. Probability
2. Stochastic Process (Random Process)
Probability Theory and
Random Processes
The theory of probability and random process is an
essential mathematical tool in the design of digital
c
Chapter 1
Introduction to
Digital Communications
Communication Systems
Communication is a process by which information is exchanged
between individuals through a common system of symbols, signs,
or behaviour.
From engineers point of view, communications
Chapter 3
Signal Space Representations
1/33
Outline
1. Vector Signal Representations
2. Signal Space Concepts
3. Gram-Schmidt Orthogonalization
2/33
Vector Spaces
A n-dimentional vector v=[v1, v2, , vn] consists of n scalar
components.
The norm of a vec