1. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Electrical Communications Systems ECE.09.331 Spring 2007 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring07/ecomms/ Lecture 7b February 28, 2007

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

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

4. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Single Sideband (SSB) Modulation Recall: DSB-SC Spectrum USSB - Signal with zero-valued spectrum for |f| < f c LSSB - Signal with zero-valued spectrum for |f| > f c -f c -B -f c -f c +B 0 f c -B f c f c +B |S(f)| f

5. S. Mandayam/ ECOMMS/ECE Dept./Rowan University The Hilbert Transform -0.5 0 0.5 1 1.5 01234567 time, t in sec » t=0:0.1:2*pi; » w=sin(t); » plot(t,w) » hold Current plot held » H=hilbert(w); » plot(t,imag(H),'r'); » xlabel('time, t in sec')

6. S. Mandayam/ ECOMMS/ECE Dept./Rowan University SSB Generation Product Modulator Carrier -90 o Phase Shift Product Modulator -90 o Phase Shift m(t)  s(t) Sideband Filter Carrier Product Modulator m(t) s(t) Phasing Method Filter Method

7. S. Mandayam/ ECOMMS/ECE Dept./Rowan University SSB Generation: Weaver’s Method

8. 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

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

10. 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

11. 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

12. 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'); »

13. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Bessel Functions %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/spring07/ecomms/demos/besselfun.m Matlab Demo Instrument Demo

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