S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Electrical
Communications Systems
0909.331.01
Spring 2005
Lab 1: Pre-lab Instruction
January 24, 2005
Shreekanth Mandayam
ECE Department
Rowan University
http://engineering.rowan.edu/~shreek/spring05/ecomms/
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
ECOMMS: Topics
Electrical Communication Systems
Signals
Discrete
Systems
Continuous
Analog
Probability
Power & Energy Signals
AM
Switching Modulator
Envelop Detector
Information
Continuous Fourier Transform
DSB-SC
Product Modulator
Coherent Detector
Costas Loop
Entropy
Discrete Fourier Transform
SSB
Weaver's Method
Phasing Method
Frequency Method
Channel Capacity
Baseband and Bandpass Signals
Frequency & Phase Modulation
Narrowband/Wideband
VCO & Slope Detector
PLL
Digital
Digital Comm Transceiver
Baseband
CODEC
Bandpass
MODEM
Source Encoding
Huffman codes
ASK
PSK
FSK
Error-control Encoding
Hamming Codes
BPSK
Sampling
PAM
QPSK
Quantization
PCM
M-ary PSK
Line Encoding
QAM
Complex Envelope
Gaussian Noise & SNR
Time Division Mux
T1 (DS1) Standards
Random Variables
Noise Calculations
Packet Switching
Ethernet
ISO 7-Layer Protocol
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
• Recall:
Plan
• Deterministic and Stochastic Waveforms
• Random Variables
• PDF and CDF
• Gaussian PDF
• Noise model
• Lab Project 1
• Part 1: Digital synthesis of arbitrary waveforms with specified
SNR
• Recall:
• How to generate frequency axis in DFT
• Lab Project 1
•
•
•
•
Part 2: CFT, Sampling and DFT (Homework!!!)
Part 3: Spectral analysis of AM and FM signals
Part 4(a): Spectral analysis of an NTSC composite video signal
Part 4(b): Spectral analysis of an ECG signal
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Recall
Waveforms
Deterministic
Stochastic
Signal
(desired)
• Probability
n
P( A)  lim  A 
n   n 
Noise
(undesired)
Random Experiment
outcome
Random Event
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Random Variable
Random
Event,
s
Random
Variable,
X
Real
Number,
a
• Definition: Let E be an experiment and S be the set of
all possible outcomes associated with the
experiment. A function, X, assigning to every element
s S, a real number, a, is called a random variable.
X(s) = a
Random
Variable
Random
Event
Real
Number
Appendix B
Prob & RV
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Parameters of an RV
F(a)
Cumulative Distribution Function (CDF) of x
F ( a )  P( x  a )
Probability Density Function (PDF) of x
dF (a )
f ( x) 
da a  x
a
f(x)
b
P (a  x  b)  F (b)  F (a )   f ( x)dx
a

 f ( x)dx  1

a
b
x
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Why are we doing this?
Input pdf
fx(x)
Transfer
Characteristic
h(x)
Output pdf
fy(y)
• For many situations, we can “model” the pdf using standard
functions
• By studying the functional forms, we can predict the expected
values of the random variable (mean, variance, etc.)
• We can predict what happens when the r.v. passes through a
system
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
PDF Model:
The Gaussian Random Variable
• The most important pdf model
• Used to model signal, noise……..
1
f ( x) 
e
2s
• m: mean;

x  m 2

s 2:
2s 2
 N (m, s )
variance
• Also called a Normal Distribution
• Central limit theorem
f(x)
2
1
2s
m
x
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Normal Distribution (contd.)
f(x)
N(m,s12)
s 22 > s 12
N(m,s22)
x
m
f(x)
N(m1,s2)
N(m2,s2)
m2 > m1
m1
m2
x
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Generating Normally Distributed
Random Variables
• Most math software provides you functions to
generate • N(0,1): zero-mean, unit-variance, Gaussian RV
• Theorem:
• N(0,s2) = sN(0,1)
• Use this for generating normally distributed r.v.’s of any
variance
• Matlab function:
• randn
• Variance
Power (how?)
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Lab Project 1:
Waveform Synthesis and
Spectral Analysis
Part 1: Digital Waveform Synthesis
http://engineering.rowan.edu/~shreek/spring05/ecomms/lab1.html
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Recall: CFT
Continuous Fourier Transform (CFT)

W (f )  Fw ( t )   w ( t ) e  j2ft dt

W (f )  X (f )  j Y (f )
W ( f )  W ( f ) e j ( f )
Amplitude
Spectrum
Frequency, [Hz]
Phase
Spectrum
Inverse Fourier Transform (IFT)
w (t)  F

W(f )   W(f ) e  j2ft df
-1

S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Recall: DFT
Equal time intervals
• Discrete Domains
• Discrete Time:
• Discrete Frequency:
k = 0, 1, 2, 3, …………, N-1
n = 0, 1, 2, 3, …………, N-1
Equal frequency intervals
• Discrete Fourier Transform
 2   nk

j
 
N 1
X[n ]   x[k ] e  N  ;
k 0
n = 0, 1, 2,….., N-1
• Inverse DFT
 2   nk
j
 
1 N 1
x[k ] 
 X[n ] e  N  ; k = 0, 1, 2,….., N-1
N n 0
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
How to get the frequency axis in the DFT
• The DFT operation just converts one set of number,
x[k] into another set of numbers X[n] - there is no
explicit definition of time or frequency
 X0 
X[ n ]   . 


X N 1 
 x0 
x[ k ]   . 


 x N 1 
(N-point FFT)
• How can we relate the DFT to the CFT and obtain
spectral amplitudes for discrete frequencies?
n=0
1
2
3
4
f=0
n=N
f = fs
fs
N
Need to
know fs
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
DFT Properties
• DFT is periodic
X[n] = X[n+N] = X[n+2N] = ………
• I-DFT is also periodic!
x[k] = x[k+N] = x[k+2N] = ……….
• Where are the “low” and “high” frequencies on the
DFT spectrum?
n=0
N/2
n=N
f=0
fs/2
f = fs
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Part 2: CFT, DFT and
Sampling
• This is homework!!!
w(t)
1V
0V
0.6 0.7 1.0
t
in ms
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Part 3: AM and FM Spectra
AM
FM
s(t) = Ac[1 + Amcos(2fmt)]cos(2fct)
s(t) = Accos[2fct + bf Amsin(2fmt)]
s(t)
s(t)
t
t
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Part 4(a): Composite NTSC Baseband
Video Signal
Color Television
Black & White Analog Television
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Part 4(b): ECG Signals
•
•
•
•
•
•
•
This experiment must be conducted with the instructor present at all
times when you are obtaining the ECG readings.
The procedure that has been outlined below has been determined to be
safe for this laboratory.
You must use an isolated power supply for powering the instrumentation
amplifier.
You must use a 10-X scope probe for recording the amplifier output on the
oscilloscope.
This objective of this experiment is compute the amplitude-frequency
spectrum of real data - this experiment does not represent a true medical
study; reading an ECG effectively takes considerable medical training.
Therefore, do not be alarmed if your data appears"different" from those
of your partners.
If you observe any allergic reactions when you attach the electrodes
(burning sensation, discomfort), remove them and rinse the area with
water.
If, for any reason, you do not want to participate in this experiment,
obtain recorded ECG data from your instructor.
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
R
ECG Signal
P
wave
T
wave
Q S
Components of the Electrocardiogram
P-Wave
P-R Interval
QRS Complex
S-T Segment
T-Wave
R-R Interval
Depolarization of the atria
Depolarization of the atria, and delay at AV junction
Depolarization of the ventricles
Period between ventricular depolarization and repolarization
Repolarization of the ventricles
Time between two ventricular depolarizations
A “Normal” ECG
Heart Rate
PR Interval
QRS Duration
QT Interval
60 - 90 bpm
0.12 - 0.20 sec
0.06 - 0.10 sec
(QTc < 0.40 sec)
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
ECG: Experiment
+9 V DC
Battery/Isolated
Power Supply
-
2
7
1
RG
INA114
8
5
6
10-X Scope
Probe
Oscilloscope
4
3
+
Right
Arm
Left
Arm
-9 V DC
Battery/Isolated
Power Supply
Drawing not to scale!
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Lab Project 1:
Waveform Synthesis and
Spectral Analysis
http://engineering.rowan.edu/~shreek/spring05/ecomms/lab1.html
S. Mandayam/ ECOMMS/ECE Dept./Rowan University
Summary