Probability and Random Variables
TWO-DIMENSIONAL RANDOM VARIABLES
TWO-DIMENSIONAL RANDOM VARIABLES
STATISTICAL AVERAGES
RANDOM PROCESSES
STATIONARITY
RANDOM PROCESSES
ERGODICITY
Baseband Pulse and
Digital Signaling
Digital signaling
Binary Signaling
Multilevel Signaling
Definitions
BaudRateD=N/To(#Symbolsperunitoftime)
BitRateR=lN/To(#Bitsperunitoftime,assumingl
bitspersymbol)
Peak Value of the error (+-) one
half of the quantize
Baseband Pulse and
Digital Signaling
Baseband Pulse and Digital Signaling
Pulse Amplitude Modulation
PAM, Pulse Amplitude modulation, conversion of an analog signal
to a pulse-type signal in which the amplitude of the pulses
contains the analog informatio
REVIEW OF LINEAR
SYSTEMS
REVIEW OF LINEAR SYSTEMS
Linear Time Invariant Systems
Impulse Response
(2.131)
(2.132)
(2.133)
Transfer Function
Power Transfer Function
(2.143)
Distortionless Transmission
Distortion Caused By a Filter
BANDLIMITED SIGNALS AND NO
In
communication systems, the received
waveform is usually categorized into the
desired part containing the information
and the extraneous or undesired part.
The desired part is called the signal, and
the undesired part is called noise.
The
waveform h
Channel Capacity
Information Measure
Information in message j
1
I = log bits
P
j
2
j
P Probability of transmitting the jth message
j
Average information:
1
H = P I = P log
P
m
j =1
m
j
j
j
2
j
R = H / T (bits / s )
Source Rate
Channel Capacity
S
C = B
Fourier Transform and Spectra
Fourier Transform and Spectra
w(t) here is a periodic function (xTo on the first slide)
Definition
W(t) here refers to the non periodic signal (x(t) on the first slide)
Fourier Transform and Spectra
C
omplex function
In gener
INTRODUCTION
E lectrical and Computer
E ngineering
Concerned with solving problems of two types:
Production or transmission of power.
Transmission or processing of information
Communication Systems Designers deal with
the transmission of information.
E le
Bandpass Signaling
Bandpass Signaling
The bandpass communication signal is obtained by modulating a baseband analog or digital
signal.
W e will use complex envelopes because with them we can represent any type of banppass
signal.
Definitions: Baseband, Ba
Phase and Frequency
Modulation
Phase Modulation and Frequency Modulation
Phase Modulation and Frequency Modulation
Phase Modulation and Frequency Modulation
Peak Frequency Deviation
Peak Phase Deviation
Phase Modulation and Frequency Modulation
Phase Modu
Baseband Pulse and
Digital Signaling
Intersymbol Interference
Raised Cosined
r=
f
f0
sin 2f 0 t cos 2f t
he = 2 f 0
2f t 1 ( 4 f t ) 2
0
The zeros of he occur at t = n /( 2 f 0 ) , n 0 ,
symbols can be inserted at the zero points
without causing ISI.