Electrical Communications Systems 0909'331'01 Spring 2005

1
Electrical Communications Systems0909.331.01
Spring 2005
Lecture 8aMarch 29, 2005

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

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Plan

• Angle Modulation Systems
• Definitions - Phase and Frequency Modulation
• Complex Envelope
• Time Domain
• Analyzing FM Signals - Battle Plan!!!!
• Single-tone FM
• Bessel Functions

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ECOMMS Topics
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Angle Modulation Systems
Phase Modulation (PM) Frequency
Modulation(FM)
Instrument Demo

• Signal Representation
• Complex Envelope
• Time Domain Representation
• Terminology
• Phase Sensitivity
• Frequency Deviation
• Instantaneous Frequency
• Phase Frequency Modulation Indices

Matlab Demo anglemod.m
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Analyzing FM Signals - Battle Plan!!!
Instrument Demo
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Bessels Differential Equation

• German mathematician and astronomer Friedrich
  Wilhelm Bessel (1784 - 1846)
• Discovered this equation while investigating
  planetary motion
• 2nd order ODE, Nonlinear, Variable Coefficients,
  Homogeneous
• Very important in applied mathematics and
  engineering
• Governing equation for problems with cylindrical
  geometries, e.g. waveguides, vibrating strings,
  and !!!!!!!

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Bessel Functions
Matlab Demo
help besselj BESSELJ Bessel function of the
first kind. J BESSELJ(NU,Z) is the Bessel
function of the first kind, J_nu(Z).The order NU
need not be an integer, but must be real.The
argument Z can be complex. The result is real
where Z is positive. x00.110
plot(x,besselj(0,x)) title('Bessel Function of
Order Zero, J_0(x)') xlabel('x')
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Bessel Functions
Matlab Demo
ECOMMS Spring 00 Classroom Demo S. Mandayam,
ECE, Rowan University clearclose
all n06 beta00.110 Jnbesselj(n,beta') pl
ot(beta',Jn) grid on xlabel('Frequency
Modulation Index \beta') ylabel('J_n(\beta)') l
egend('J_0(\beta)','J_1(\beta)','J_2(\beta)', 'J_3
(\beta)','J_4(\beta)','J_5(\beta)','J_6(\beta)')
title('J_n(\beta) Spectral Amplitudes of an FM
signal at f_c \pm nf_m')
http//engineering.rowan.edu/shreek/spring05/ecom
ms/demos/besselfun.m
Instrument Demo
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FM Signal Spectrum
Single-tone FM Signal
Single-tone FM Spectrum
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Summary