Electrical Communications Systems 0909.331.01 Spring 2005

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Electrical Communications Systems0909.331.01
Spring 2005
Lab 1 Pre-lab InstructionJanuary 24, 2005

• Shreekanth Mandayam
• ECE Department
• Rowan University
• http//engineering.rowan.edu/shreek/spring05/ecom
  ms/

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ECOMMS Topics
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Plan

• Recall
• 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

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Recall

• Probability

Random Experiment
outcome
Random Event
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Random Variable

• 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

Real Number
Random Variable
Appendix B Prob RV
Random Event
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Parameters of an RV
F(a)
a
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Why are we doing this?
Transfer Characteristic h(x)
Input pdf fx(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

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PDF Model The Gaussian Random Variable

• The most important pdf model
• Used to model signal, noise..
• m mean s2 variance
• Also called a Normal Distribution
• Central limit theorem

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Normal Distribution (contd.)
f(x)
N(m1,s2)
N(m2,s2)
m2 gt m1
x
m1
m2
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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?)

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Lab Project 1Waveform Synthesis and Spectral
Analysis Part 1 Digital Waveform Synthesis
http//engineering.rowan.edu/shreek/spring05/ecom
ms/lab1.html
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Recall CFT
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Recall DFT

• Discrete Domains
• Discrete Time k 0, 1, 2, 3, , N-1
• Discrete Frequency n 0, 1, 2, 3, , N-1
• Discrete Fourier Transform
• Inverse DFT

Equal frequency intervals
n 0, 1, 2,.., N-1
k 0, 1, 2,.., N-1
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How to get the frequency axis in the DFT

• The DFT operation just converts one set of
  number, xk into another set of numbers Xn -
  there is no explicit definition of time or
  frequency
• How can we relate the DFT to the CFT and obtain
  spectral amplitudes for discrete frequencies?

(N-point FFT)
Need to know fs
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DFT Properties

• DFT is periodic
• Xn XnN Xn2N
• I-DFT is also periodic!
• xk xkN xk2N .
• Where are the low and high frequencies on the
  DFT spectrum?

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Part 2 CFT, DFT and Sampling

• This is homework!!!

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Part 3 AM and FM Spectra

• AM
• s(t) Ac1 Amcos(2pfmt)cos(2pfct)

• FM
• s(t) Accos2pfct bf Amsin(2pfmt)

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Part 4(a) Composite NTSC Baseband Video Signal
Color Television
Black White Analog Television
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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.

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ECG Signal
Components of the Electrocardiogram P-Wave Depo
larization of the atria P-R Interval Depolarizatio
n of the atria, and delay at AV junction QRS
Complex Depolarization of the ventricles S-T
Segment Period between ventricular depolarization
and repolarization T-Wave Repolarization of the
ventricles R-R Interval Time between two
ventricular depolarizations A Normal
ECG Heart Rate 60 - 90 bpm PR Interval 0.12 -
0.20 sec QRS Duration 0.06 - 0.10 sec QT
Interval (QTc lt 0.40 sec)
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ECG Experiment
Drawing not to scale!
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Lab Project 1Waveform Synthesis and Spectral
Analysis
http//engineering.rowan.edu/shreek/spring05/ecom
ms/lab1.html
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Summary