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Electrical Communications Systems 0909.331.01 Spring 2005

This lecture explores angle modulation systems, including phase and frequency modulation. It covers signal representation, complex envelope, time domain representation, terminology, phase sensitivity, frequency deviation, and instantaneous frequency.

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Electrical Communications Systems 0909.331.01 Spring 2005

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  1. Electrical Communications Systems0909.331.01Spring 2005 Lecture 8aMarch 29, 2005 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring05/ecomms/

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

  3. ECOMMS: Topics

  4. Angle Modulation Systems • Signal Representation • Complex Envelope • Time Domain Representation • Terminology • Phase Sensitivity • Frequency Deviation • Instantaneous Frequency • Phase & Frequency Modulation Indices Phase Modulation (PM) Frequency Modulation(FM) Instrument Demo Matlab Demo: anglemod.m

  5. Signals Systems • Time Domain • Complex Envelope • Spectrum • Single-tone FM • Narrowband FM • Wideband FM • Bessel Functions • Power Performance Transmitters Receivers Standards Modulation Index Efficiency Bandwidth Noise Analyzing FM Signals - Battle Plan!!! Instrument Demo

  6. Bessel’s 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 …………!!!!!!!

  7. 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. » » » » x=0:0.1:10; » plot(x,besselj(0,x)); » title('Bessel Function of Order Zero, J_0(x)'); » xlabel('x'); »

  8. Bessel Functions Matlab Demo %ECOMMS Spring 00 Classroom Demo %S. Mandayam, ECE, Rowan University clear;close all; n=0:6; beta=0:0.1:10; Jn=besselj(n,beta'); plot(beta',Jn); grid on; xlabel('Frequency Modulation Index: \beta'); ylabel('J_n(\beta)'); legend('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/ecomms/demos/besselfun.m Instrument Demo

  9. J1(b) |S(f)| / (Ac/2) J2(b) J3(b) J0(b) 0fc-3fm fc-2fm fc-fm fc fc+fm fc+2fm fc+3fm f FM Signal & Spectrum Single-tone FM Signal Single-tone FM Spectrum

  10. Summary

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