S Mandayam ECOMMSECE Dept Rowan University Electrical Communications

S. Mandayam/ ECOMMS/ECE Dept. /Rowan University Electrical Communications Systems ECE. 09. 331 Spring 2008 Lecture 8 a March 11, 2008 Shreekanth Mandayam ECE Department Rowan University http: //engineering. rowan. edu/~shreek/spring 08/ecomms/

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

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

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

S. Mandayam/ ECOMMS/ECE Dept. /Rowan University The Hilbert Transform 1. 5 » 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') 1 0. 5 0 -0. 5 -1 0 1 2 3 4 time, t in sec 5 6 7

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

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

S. Mandayam/ ECOMMS/ECE Dept. /Rowan University Angle Modulation Systems Phase Modulation (PM) Frequency Modulation(FM) • Signal Representation Instrument Demo • Complex Envelope • Time Domain Representation • Terminology • • Phase Sensitivity Frequency Deviation Instantaneous Frequency Phase & Frequency Modulation Indices Matlab Demo: anglemod. m

S. Mandayam/ ECOMMS/ECE Dept. /Rowan University Analyzing FM Signals Battle Plan!!! Instrument Demo Signals Systems Time Domain Performance Complex Envelope Transmitters Spectrum Receivers • Single-tone FM • Narrowband FM Standards • Wideband FM • Bessel Functions Power Modulation Index Efficiency Bandwidth Noise

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'); »

S. Mandayam/ ECOMMS/ECE Dept. /Rowan University Bessel Functions Matlab 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/spring 08/ecomms/demos/besselfun. m Instrument Demo

S. Mandayam/ ECOMMS/ECE Dept. /Rowan University FM Signal & Spectrum Single-tone FM Signal Single-tone FM Spectrum J 1(b) |S(f)| / (Ac/2) J 2(b) J 0(b) 0 J 3(b) fc-3 fm fc-2 fm fc-fm fc fc+fm fc+2 fm fc+3 fm f

S. Mandayam/ ECOMMS/ECE Dept. /Rowan University Summary