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Electrical Communications Systems ECE.09.331 Spring 2007. Lecture 8b March 7, 2007. Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring07/ecomms/. Plan. Analyzing FM Signals - Battle Plan!!!! Single-tone FM Bessel Functions FM Spectra

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Electrical Communications Systems ECE.09.331 Spring 2007


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    1. Electrical Communications SystemsECE.09.331Spring 2007 Lecture 8bMarch 7, 2007 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring07/ecomms/

    2. Plan • Analyzing FM Signals - Battle Plan!!!! • Single-tone FM • Bessel Functions • FM Spectra • Power etc. • Digital Communications • Introduction • Digital Communications Transceiver (CODEC/MODEM)

    3. ECOMMS: Topics

    4. 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) Instrument Demo Matlab Demo: anglemod.m

    5. 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 Analyzing FM Signals - Battle Plan!!! Instrument Demo

    6. 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. 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. Bessel Functions Matlab Demo %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 Instrument Demo

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

    10. ECOMMS: Topics

    11. 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. 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. Principle Digital message 1 1 1 0 1 0……… 0 0 Digital code Analog message modulate 1 0 1 0 Sinusoidal carrier AM FM PM AM & PM

    14. Message 1 Message 1 Multiplexer 2 Demultiplexer 1 2 3 1 S 2 3 S Message 2 Message 2 Message 3 Message 3 3 H H 1 Depacket-izing Message 1 2 H Message 1 3 H H 1 Depacket-izing Packetizing Message 2 Message 2 2 H 3 H Message 3 Depacket-izing H 1 Message 3 2 H Digital Communication Paradigms Circuit Switching Sync bits Packet Switching Header bits

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

    16. Summary