1. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Electrical Communications Systems ECE.09.331 Spring 2011 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring11/ecomms/ Lecture 9a March 23, 2011

2. S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityPlan Analyzing FM Signals Single-tone FM Narrowband FM Wideband FM Bessel Functions Digital Communications Introduction Digital Communications Transceiver (CODEC/MODEM) Digital Baseband Communications Source Encoding Huffman Coding

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

4. 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

5. 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 …………!!!!!!!

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 11 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/spring11/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 University ECOMMS: Topics

10. 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

11. 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?

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

13. 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

14. 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

15. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Source Encoding Why are we doing this? Analog Message A/D Converter Digital Source Encoder Source Symbols (0/1) Source Entropy Encoded Symbols (0/1) Source-Coded Symbol Entropy

16. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Source Encoding Requirements Decrease L av Unique decoding Instantaneous decoding

17. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Huffman Coding 2-Step Process Reduction List symbols in descending order of probability Reduce the two least probable symbols into one symbol equal to their combined probability Reorder in descending order of probability at each stage Repeat until only two symbols remain Splitting Assign 0 and 1 to the final two symbols remaining and work backwards Expand code at each split by appending a 0 or 1 to each code word Example m(j)ABCDEFGH P(j)0.10.180.40.050.060.10.070.04

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