Electrical Communications Systems ECE.09.331 Spring 2008 Lecture 8a March 11, 2008 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring08/ecomms/

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

ECOMMS: Topics

Single Sideband (SSB) Modulation Recall: DSB-SC Spectrum USSB - Signal with zero-valued spectrum for |f| < fc LSSB - Signal with zero-valued spectrum for |f| > fc -fc-B -fc -fc+B 0 fc-B fc fc+B |S(f)| f

The Hilbert Transform time, t in sec -1 -0.5 0.5 1 1.5 2 3 4 5 6 7 0.5 1 1.5 2 3 4 5 6 7 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')

SSB Generation S Phasing Method Filter Method m(t) s(t) m(t) s(t) Product Modulator Carrier -90o Phase Shift m(t) S s(t) Filter Method Sideband Filter Carrier Product Modulator m(t) s(t)

SSB Generation: Weaver’s Method

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

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

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');

Bessel Functions Matlab Demo Instrument Demo %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 Instrument Demo

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

Summary