1. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Electrical Communications Systems ECE.09.331 Spring 2008 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring08/ecomms/ Lecture 9a March 25, 2008

2. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Plan Angle Modulation Systems Definitions - Phase and Frequency Modulation Complex Envelope Time Domain Analyzing FM Signals - Battle Plan!!!! FM Spectrum Single-tone FM Bessel Functions Wideband FM

3. S. Mandayam/ ECOMMS/ECE Dept./Rowan University ECOMMS: Topics

4. S. Mandayam/ ECOMMS/ECE Dept./Rowan University 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) Matlab Demo: anglemod.m Instrument Demo

5. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Analyzing FM Signals - Battle Plan!!! Instrument Demo 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

6. S. Mandayam/ ECOMMS/ECE Dept./Rowan University 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'); »

7. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Bessel Functions %ECOMMS Spring 08 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/spring08/ecomms/demos/besselfun.m Matlab Demo Instrument Demo

8. S. Mandayam/ ECOMMS/ECE Dept./Rowan University FM Signal & Spectrum Single-tone FM Signal Single-tone FM Spectrum 0 f c -3f m f c -2f m f c -f m f c f c +f m f c +2f m f c +3f m |S(f)| / (A c /2) f J0()J0() J1()J1() J2()J2() J3()J3()

9. S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversitySummary