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 8b March 7, 2007

2. S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityPlan Analyzing FM Signals - Battle Plan!!!! Single-tone FM Bessel Functions FM Spectra Power etc. Digital Communications Introduction Digital Communications Transceiver (CODEC/MODEM)

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’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. 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'); »

8. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Bessel Functions %ECOMMS Spring 07 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

9. 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()

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

11. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Digital Communications Some Milestones Claude Shannon, 1948 X.25 (Telephony) IEEE 802.3 (Ethernet) ARPANET, 1969 IEEE 802.5 (FDDI) ISO-OSI 7-layer Network Reference Model CDMA GSM VOIP SIP protocols.com

12. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Digital Communications: Rationale Information Theory: What is the fundamental limit on the compression and refinement of information generated by the source? What is the fundamental limit on the transmission rate of information over a noisy channel? How do we approach these limits?

13. S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityPrinciple 1 0 1 0……… 1 0 Analog message Digital code Digital message Sinusoidal carrier modulate AM FM PM AM & PM 1 0

14. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Digital Communication Paradigms Multiplexer Message 2 Message 3 Message 1 1 2 3 S 1 2 2 3 S Demultiplexer Message 2 Message 3 Message 1 Packetizing Message 2 Message 3 Message 1 1H H 2 3 H H 2 1H 3 H H 2 1H 3 H Message 2 Message 3 Message 1 Depacket -izing Circuit Switching Packet Switching Sync bits Header bits

15. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Digital Communications Transceiver Anti- aliasing Filter SamplingQuantization Data Encryption Encoder Source Encoder Error Control Encoder Channel/ Line Encoder Modulator MUX Audio Amp Source Decoder Data Encryption Decoder Error Control Decoder Equalization / Decision Circuits Demod- ulator DEMUX Reconstruction/ DAC ADC CODEC MODEM Analog o/p Multiple access channel Analog i/p

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