ELE/STAT 485 SIGNAL ANALYSIS AND COMMUNICATION SYSTEMS

Fall 1990-91

Professor Sergio Verdú

0. INTRODUCTION

Electrical Communication Systems Basic Elements of a Communication System Bandwidth limitation, Noise and other noinideal effects Modulation: motivation and categories Chronology of Communication theory and practice

I. SIGNAL ANALYSIS REVIEW

I1. Signal Classifications - I2. Fourier Transform Delta Function Fourier Transform: Definition and Properties Parseval's Theorem Transform Theorems Convolution Fourier Transform of Periodic Signals - I3. Linear Systems and Transforms Definition and examples Impulse response and superposition integral Time-invariant systems Transfer Function - I4. Correlation and Power Spectrum Scalar (inner) product and norm Cauchy-Schwarz inequality Autocorrelation and Crosscorrelation Function Power and Energy Spectral Density Input-Output Relations - I5. Hilbert Transform

II. MODULATION

II1. Continuous-Wave Modulation - II1.1 Linear DSB AM Power Analysis of AM modulation Practical modulators for AM and DSB SSB VSB II1.2 Exponential: PM and FM Time-Domain Definition Spectrum Analysis with sinusoidal message FM Bandwidth FM Modulation FM Demodulation FM Stereo -II1.3 Superheterodyne Receiver - II2. Pulse Modulation of Digital Data - II2.1 OOK, FSK, PSK, DPSK, PAM - II2.2 Quadrature Modulation: QPSK, QAM - II2.3 Spread-Spectrum - II3. Multiplexing: FDM, TDM - II4. Pulse Modulation of Analog Signals Ideal Sampling Practical Sampling Quantization PCM Delta Modulation Adaptive Delta Modulation

III. PROBABILITY AND RANDOM PROCESSES

III1. Introduction and Axioms Measuring Sets Set functions Axioms and Properties - III2. Independence and Conditional Probabilities. Independent Events Bernouilli's formula Conditional Probability Basic formulas: total probability, Bayes', etc. - III3. Random Variables, Distribution and Density Functions. Definition of Random Variable Cumulative Distribution Function Classification of Random Variables Probability Density Functions Conditional Distributions. - III4. Joint Distribution and Density Functions. Definition Independent Random Variables Transformation of Random Variables - III5. Statistical Averages Expectation of a Random Variable Moments Chebyshev's inequality Law of large numbers Characteristic Function pdf of sums of independent random variables and CLT. Moment Theorem - III6. Random Processes Definition First Order Statistics Second Order Statistics Nth Order Statistics Stationarity and Wide-sense Stationarity Poisson process Gaussian process - III7. Correlation and Power Spectral Density. Definitions Wiener and Khintchine Theorem Time averages and ergodicity - III8. Linear Systems and Random Processes. - III9. Representation of Narrowband Noise

IV. ANALYSIS OF COMMUNICATION SYSTEMS

IV1. SNR of CW Modulation Systems - IV1.1 SNR in Coherent Demodulation of AM, DSB, SSB - IV1.2 SNR in AM Envelope Detection - IV1.3 SNR in Exponential Modulation. FM Threshold Effect. Pre/De- emphasis - IV2. Probability of Error in Digital Pulse Modulation Probability of error with rectangular signals and integrator Brownian Motion Arbitrary Signal Shapes and Arbitrary linear receiver System optimization: Threshold and Matched Filter Optimality of Antipodal signals Probability of error of PSK, OOK, FSK, etc. - IV3. A case study: The Digital Audio Compact Disc