Digital Communications Fundamentals and Applications by Bernard Sklar

Book Name:Digital Communications  Fundamentals and Applications

Author: Bernard Sklar

Edition:Second
Pages: 1032

Click here to download

Contents

PREFACE
1 SIGNALS AND SPECTRA                                                                                
1.1 Digital Communication Signal Processing,                                                    
1.1.1 Why Digital?,                                                                                                
1.1.2 Typical Block Diagram and Transformations,
1.1.3 Basic Digital Communication Nomenclature,
1.1.4 Digital versus Analog Performance Criteria,
1.2 Classification of Signals,
1.2.1 Deterministic and Random Signals,
1.2.2 Periodic and Nonperiodic Signals,
1.2.3 Analog and Discrete Signals,
1.2.4 Energy and Power Signals,
1.2.5 The Unit Impulse Function,
1.3 Spectral Density,
1.3.1 Energy Spectral Density,
1.3.2 Power Spectral Density,
1.4 Autocorrelation,
1.4.1 Autocorrelation of an Energy Signal,
1.4.2 Autocorrelation of a Periodic (Power) Signal,
1.5 Random Signals,
1.5.1 Random Variables,
1.5.2 Random Processes,
1.5.3 Time Averaging and Ergodicity,
1.5.4 Power Spectral Density of a Random Process,
1.5.5 Noise in Communication Systems,
1.6 Signal Transmission through Linear Systems,
1.6.1 Impulse Response,
1.6.2 Frequency Transfer Function,
1.6.3 Distortionless Transmission,
1.6.4 Signals, Circuits, and Spectra,
1.7 Bandwidth of Digital Data,
1.7.1 Baseband versus Bandpass,
1.7.2 The Bandwidth Dilemma,
1.8 Conclusion,
2 FORMATTING AND BASEBAND MODULATION
2.1 Baseband Systems,
2.2 Formatting Textual Data (Character Coding),
2.3 Messages, Characters, and Symbols,
2.3.7 Example of Messages, Characters, and Symbols,
2.4 Formatting Analog Information,
2.4.1 The Sampling Theorem,
2.4.2 Aliasing,
2.4.3 Why Oversample?
2.4.4 Signal Interface for a Digital System,
2.5 Sources of Corruption,
2.5.7 Sampling and Quantizing Effects,
2.5.2 Channel Effects,
2.5.3 Signal-to-Noise Ratio for Quantized Pulses,
2.6 Pulse Code Modulation,
2.7 Uniform and Nonuniform Quantization,
2.7.7 Statistics of Speech Amplitudes,
2.7.2 Nonuniform Quantization,
2.7.3 Companding Characteristics,
2.8 Baseband Modulation,
2.8.1 Waveform Representation of Binary Digits,
2.8.2 PCM Waveform Types,
2.8.3 Spectral Attributes of PCM Waveforms,
2.8.4 Bits per PCM Word and Bits per Symbol,
2.8.5 M-ary Pulse Modulation Waveforms,
2.9 Correlative Coding,
2.9.7 Duobinary Signaling,
2.9.2 Duobinary Decoding,
2.9.3 Preceding,
2.9.4 Duobinary Equivalent Transfer Function,
2.9.5 Comparison of Binary with Duobinary Signaling,
2.9.6 Poly binary Signaling,
2.10 Conclusion,
3 BASED AND DEMODULATION/DETECTION
3.1 Signals and Noise,
3.1.1 Error-Performance Degradation in Communication Systems,
3.1.2 Demodulation and Detection,
3.1.3 A Vectorial View of Signals and Noise,
3.1.4 The Basic SNR Parameter for Digital Communication Systems,
3.1.5 Why Eb/N0 Is a Natural Figure of Merit,
3.2 Detection of Binary Signals in Gaussian Noise,
3.2.1 Maximum Likelihood Receiver Structure,
3.2.2 The Matched Filter,
3.2.3 Correlation Realization of the Matched Filter,
3.2.4 Optimizing Error Performance,
3.2.5 Error Probability Performance of Binary Signaling,
3.3 Intersymbol Interference,
3.3.1 Pulse Shaping to Reduce ISI,
3.3.2 Two Types of Error-Performance Degradation,
3.3.3 Demodulation/Detection of Shaped Pulses,
3.4 Equalization,
3.4.1 Channel Characterization,
3.4.2 Eye Pattern
3.4.3 Equalizer Filter Types,
3.4.4 Preset and Adaptive Equalization,
3.4.5 Filter Update Rate,
3.5 Conclusion,
4 BANDPASS MODULATION AND DEMODULATION/DETECTION
4.1 Why Modulate?
4.2 Digital Bandpass Modulation Techniques,
4.2.1 Phasor Representation of a Sinusoid,
4.2.2 Phase Shift Keying,
4.2.3 Frequency Shift Keying,
4.2.4 Amplitude Shift Keying,
4.2.5 Amplitude Phase Keying,
4.2.6 Waveform Amplitude Coefficient,
4.3 Detection of Signals in Gaussian Noise,
4.3.1 Decision Regions,
4.3.2 Correlation Receiver,
4.4 Coherent Detection,
4.4.1 Coherent Detection of PSK,
4.4.2 Sampled Matched Filter,
4.4.3 Coherent Detection of Multiple Phase Shift Keying,
4.4.4 Coherent Detection of FSK,
4.5 Noncoherent Detection,
4.5.1 Detection of Differential PSK,
4.5.2 Binary Differential PSK Example,
4.5.3 Noncoherent Detection of FSK,
4.5.4 Required Tone Spacing for Noncoherent Orthogonal FSK,
4.6 Complex Envelope,
4.6.1 Quadrature Implementation of a Modulator,
4.6.2 D8PSK Modulator Example,
4.6.3 D8PSK Demodulator Example,
4.7 Error Performance for Binary Systems,
4.7.1 Probability of Bit Error for Coherently Detected BPSK,
4.7.2 Probability of Bit Error for Coherently Detected
Differentially Encoded Binary PSK,
4.7.3 Probability of Bit Error for Coherently Detected
Binary Orthogonal FSK,
4.7.4 Probability of Bit Error for Noncoherently Detected
Binary Orthogonal FSK,
4.7.5 Probability of Bit Error for Binary DPSK,
4.7.6 Comparison of Bit Error Performance for Various
Modulation Types,
4.8 M-ary Signaling and Performance,
4.8.1 Ideal Probability of Bit Error Performance,
4.8.2 M-ary Signaling,
4.8.3 Vectorial View of MPSK Signaling,
4.8.4 BPSK and QPSK Have the Same Bit Error Probability,
4.8.5 Vectorial View of MFSK Signaling,
4.9 Symbol Error Performance for M-ary Systems (M > 2),
4.9.1 Probability of Symbol Error for MPSK,
4.9.2 Probability of Symbol Error for MFSK,
4.9.3 Bit Error Probability versus Symbol Error Probability
for Orthogonal Signals,
4.9.4 Bit Error Probability versus Symbol Error Probability
for Multiple Phase Signaling,
4.9.5 Effects of Intersymbol Interference,
4.10 Conclusion,
5 COMMUNICATIONS LINK ANALYSIS 
5.1 What the System Link Budget Tells the System Engineer,
5.2 The Channel,
5.2.7 The Concept of Free Space,
5.2.2 Error-Performance Degradation,
5.2.3 Sources of Signal Loss and Noise,
5.3 Received Signal Power and Noise Power,
5.3J The Range Equation,
5.3.2 Received Signal Power as a Function of Frequency,
5.3.3 Path Loss is Frequency Dependent,
5.3.4 Thermal Noise Power,
5.4 Link Budget Analysis,
5.4.1 Two E//NQ Values of Interest,
5.4.2 Link Budgets are Typically Calculated in Decibels,
5.4.3 How Much Link Margin is Enough?
5.4.4 Link Availability,
5.5 Noise Figure, Noise Temperature, and System Temperature,
5.5 J Noise Figure,
5.5.2 Noise Temperature,
5.5.3 Line Loss,
5.5.4 Composite Noise Figure and Composite Noise Temperature,
5.5.5 System Effective Temperature,
5.5.6 Sky Noise Temperature,
5.6 Sample Link Analysis,
5.6.1 Link Budget Details,
5.6.2 Receiver Figure of Merit,
5.6.3 Received Isotropic Power,
5.7 Satellite Repeaters,
5.7.7 Nonregenerative Repeaters,
5.7.2 Nonlinear Repeater Amplifiers,
5.8 System Trade-Offs,
5.9 Conclusion,
6 CHANNEL CODING: PART 1 
6.1 Waveform Coding and Structured Sequences,
6.1.1 Antipodal and Orthogonal Signals,
6.1.2 M-ary Signaling,
6.1.3 Waveform Coding,
6.1.4 Waveform-Coding System Example,
6.2 Types of Error Control,
6.2.1 Terminal Connectivity,
6.2.2 Automatic Repeat Request,
6.3 Structured Sequences,
6.3.1 Channel Models,
6.3.2 Code Rate and Redundancy,
6.3.3 Parity Check Codes,
6.3.4 Why Use Error-Correction Coding?
6.4 Linear Block Codes,
6.4.1 Vector Spaces,
6.4.2 Vector Subspaces,
6.4.3 A (6, 3) Linear Block Code Example,
6.4.4 Generator Matrix,
6.4.5 Systematic Linear Block Codes,
6.4.6 Parity-Check Matrix,
6.4.7 Syndrome Testing,
6.4.8 Error Correction,
6.4.9 Decoder Implementation,
6.5 Error-Detecting and Correcting Capability,
6.5.1 Weight and Distance of Binary Vectors,
6.5.2 Minimum Distance of a Linear Code,
6.5.3 Error Detection and Correction,
6.5.4 Visualization of a 6-Tuple Space,
6.5.5 Erasure Correction,
6.6 Usefulness of the Standard Array,
6.6.1 Estimating Code Capability,
6.6.2 An (n, k) Example,
6.6.3 Designing the (8, 2) Code,
6.6.4 Error Detection versus Error Correction Trade-Offs,
6.6.5 The Standard Array Provides Insight,
6.7 Cyclic Codes,
6.7.7 Algebraic Structure of Cyclic Codes,
6.7.2 Binary Cyclic Code Properties,
6.7.3 Encoding in Systematic Form,
6.7.4 Circuit for Dividing Polynomials,
6.7.5 Systematic Encoding with an (n - k)-Stage Shift Register,
6.7.6 Error Detection with an (n - k)-Stage Shift Register,
6.8 Weil-Known Block Codes,
6.8.1 Hamming Codes,
6.8.2 Extended Golay Code,
6.8.3 BCH Codes,
6.9 Conclusion,
7 CHANNEL CODING: PART 2 
7.1 Convolutional Encoding,
7.2 Convolutional Encoder Representation,
7.2.1 Connection Representation,
7.2.2 State Representation and the State Diagram,
7.2.3 The Tree Diagram,
7.2.4 The Trellis Diagram,
7.3 Formulation of the Convolutional Decoding Problem,
7.3.1 Maximum Likelihood Decoding,
7.3.2 Channel Models: Hard versus Soft Decisions,
7.3.3 The Viterbi Convolutional Decoding Algorithm,
7.3.4 An Example of Viterbi Convolutional Decoding,
7.3.5 Decoder Implementation,
7.3.6 Path Memory and Synchronization,
7.4 Properties of Convolutional Codes,
7.4.1 Distance Properties of Convolutional Codes,
7.4.2 Systematic and Nonsystematic Convolutional Codes,
7.4.3 Catastrophic Error Propagation in Convolutional Codes,
7.4.4 Performance Bounds for Convolutional Codes,
7.4.5 Coding Gain,
7.4.6 Best Known Convolutional Codes,
7.4.7 Convolutional Code Rate Trade-Off,
7.4.8 Soft-Decision Viterbi Decoding,
7.5 Other Convolutional Decoding Algorithms,
7.5.1 Sequential Decoding,
7.5.2 Comparisons and Limitations of Viterbi and Sequential Decoding,
7.5.3 Feedback Decoding,
7.6 Conclusion,
8 CHANNEL CODING: PART 3 
8.1 Reed-Solomon Codes,
8.1.1 Reed-Solomon Error Probability,
8.1.2 Why R-S Codes Perform Well Against Burst Noise,
8.1.3 R-S Performance as a Function of Size,
Redundancy, and Code Rate,
8.1.4 Finite Fields
8.1.5 Reed-Solomon Encoding,
8.1.6 Reed-Solomon Decoding,
8.2 Interleaving and Concatenated Codes,
8.2.1 Block Interleaving,
8.2.2 Convolutional Interleaving,
8.2.3 Concatenated Codes,
8.3 Coding and Interleaving Applied to the Compact Disc
Digital Audio System,
8.3.1 CIRC Encoding,
8.3.2 CIRC Decoding,
8.3.3 Interpolation and Muting,
8.4 Turbo Codes,
8.4.1 Turbo Code Concepts,
8.4.2 Log-Likelihood Algebra,
8.4.3 Product Code Example,
8.4.4 Encoding with Recursive Systematic Codes,
8.4.5 A Feedback Decoder,
8.4.6 The MAP Decoding Algorithm,
8.4.7 MAP Decoding Example,
8.5 Conclusion,
Appendix 8A The Sum of Log-Likelihood Ratios,
9 MODULATION AND CODING TRADE-OFFS 
9.1 Goals of the Communications System Designer,
9.2 Error Probability Plane,
9.3 Nyquist Minimum Bandwidth,
9.4 Shannon-Hartley Capacity Theorem,
9.4.1 Shannon Limit,
9.4.2 Entropy,
9.4.3 Equivocation and Effective Transmission Rate,
9.5 Bandwidth Efficiency Plane,
9.5.7 Bandwidth Efficiency ofMPSK and MFSK Modulation,
9.5.2 Analogies Between Bandwidth-Efficiency
and Error Probability Planes,
9.6 Modulation and Coding Trade-Offs,
9.7 Defining, Designing, and Evaluating Digital
Communication Systems,
9.7.7 M-ary Signaling,
9.7.2 Bandwidth-Limited Systems,
9.7.3 Power-Limited Systems,
9.7.4 Requirements for MPSK and MFSK Signaling,
9.7.5 Bandwidth-Limited Uncoded System Example,
9.7.6 Power-Limited Uncoded System Example,
9.7.7 Bandwidth-Limited and Power-Limited
Coded System Example,
9.8 Bandwidth-Efficient Modulation,
9.5.7 QPSK and Offset QPSK Signaling,
9.8.2 Minimum Shift Keying,
9.8.3 Quadrature Amplitude Modulation,
9.9 Modulation and Coding for Bandlimited Channels,
9.9.7 Commercial Telephone Modems,
9.9.2 Signal Constellation Boundaries
9.9.3 Higher Dimensional Signal Constellations,
9.9.4 Higher-Density Lattice Structures,
9.9.5 Combined Gain: N-Sphere Mapping and Dense Lattice,
9.10 Trellis-Coded Modulation,
9.70.7 The Idea Behind Trellis-Coded Modulation (TCM),
9.10.2 TCM Encoding,
9.10.3 TCM Decoding,
9.10.4 Other Trellis Codes,
9.10.5 Trellis-Coded Modulation Example,
9.10.6 Multi-Dimensional Trellis-Coded Modulation,
9.11 Conclusion,
10 SYNCHRONIZATION 
10.1 Introduction,
10.1.1 Synchronization Defined,
10.1.2 Costs versus Benefits,
10.1.3 Approach and Assumptions,
10.2 Receiver Synchronization,
10.2.1 Frequency and Phase Synchronization,
10.2.2 Symbol Synchronization—Discrete Symbol Modulations,
10.2.3 Synchronization with Continuous-Phase Modulations (CPM),
10.2.4 Frame Synchronization,
10.3 Network Synchronization,
10.3.1 Open-Loop Transmitter Synchronization,
10.3.2 Closed-Loop Transmitter Synchronization,
10.4 Conclusion,
11 MULTIPLEXING AND MULTIPLE ACCESS
11.1 Allocation of the Communications Resource,
11.1.1 Frequency-Division Multiplexing/Multiple Access,
11.1.2 Time-Division Multiplexing/Multiple Access,
11.1.3 Communications Resource Channelization,
11.1.4 Performance Comparison ofFDMA and TDMA,
11.1.5 Code-Division Multiple Access,
11.1.6 Space-Division and Polarization-Division Multiple Access,
11.2 Multiple Access Communications System and Architecture,
11.2.1 Multiple Access Information Flow,
11.2.2 Demand Assignment Multiple Access,
11.3 Access Algorithms,
11.3.1 ALOHA
11.3.2 Slotted ALOHA,
11.3.3 Reservation-ALOHA,
11.3.4 Performance Comparison ofS-ALOHA and R-ALOHA,
11.3.5 Polling Techniques,
11.4 Multiple Access Techniques Employed with INTELSAT,
11.4.1 Preassigned FDM/FM/FDMA or MCPC Operation,
11.4.2 MCPC Modes of Accessing an INTELSA T Satellite,
11.4.3 SPADE Operation,
11.4.4 TDMA in INTELSAT,
11.4.5 Satellite-Switched TDMA in INTELSAT,
11.5 Multiple Access Techniques for Local Area Networks,
11.5.1 Carrier-Sense Multiple Access Networks,
11.5.2 Token-Ring Networks,
11.5.3 Performance Comparison of CSMA/CD and Token-Ring Networks,
11.6 Conclusion,
12 SPREAD-SPECTRUM TECHNIQUES 
12.1 Spread-Spectrum Overview,
12.1.1 The Beneficial Attributes of Spread-Spectrum Systems,
12.1.2 A Catalog of Spreading Techniques,
12.1.3 Model for Direct-Sequence Spread-Spectrum
Interference Rejection,
12.1.4 Historical Background,
12.2 Pseudonoise Sequences,
72.2.1 Randomness Properties,
12.2.2 Shift Register Sequences,
12.2.3 PN Autocorrelation Function,
12.3 Direct-Sequence Spread-Spectrum Systems,
12.3.1 Example of Direct Sequencing,
12.3.2 Processing Gain and Performance,
12.4 Frequency Hopping Systems,
12.4.1 Frequency Hopping Example,
12.4.2 Robustness,
12.4.3 Frequency Hopping with Diversity,
12.4.4 Fast Hopping versus Slow Hopping,
12.4.5 FFH/MFSK Demodulator,
12.4.6 Processing Gain,
12.5 Synchronization,
12.5.1 Acquisition,
12.5.2 Tracking,
12.6 Jamming Considerations,
12.6.1 The Jamming Game,
12.6.2 Broadband Noise Jamming,
12.6.3 ^Partial-Band Noise Jamming,
12.6.4 . Multiple-Tone Jamming,
12.6.5 Pulse Jamming,
12.6.6 Repeat-Back Jamming,
12.6.7 BLADES System,
12.7 Commercial Applications,
12.7.1 Code-Division Multiple Access,
12.7.2 Multipath Channels,
12.7.3 The FCC Part 15 Rules for Spread-Spectrum Systems,
12.7.4 Direct Sequence versus Frequency Hopping,
12.8 Cellular Systems,
12.8.1 Direct Sequence CDMA,
12.8.2 Analog FM versus TDMA versus CDMA,
12.8.3 Interference-Limited versus Dimension-Limited Systems,
12.8.4 IS-95 CDMA Digital Cellular System,
12.9 Conclusion,
13 SOURCE CODING 
13.1 Sources,
13.1.1 Discrete Sources,
13.1.2 Waveform Sources,
13.2 Amplitude Quantizing,
13.2.1 Quantizing Noise,
13.2.2 Uniform Quantizing,
13.2.3 Saturation,
13.2.4 Dithering,
13.2.5 Nonuniform Quantizing,
13.3 Differential Pulse-Code Modulation,
13.3.1 One-Tap Prediction,
13.3.2 N-Tap Prediction,
13.3.3 Delta Modulation,
13.3.4 Sigma-Delta Modulation,
13.3.5 Sigma-Delta A-to-D Converter (ADC),
13.3.6 Sigma-Delta D-to-A Converter (DAC),
13.4 Adaptive Prediction,
13.4.1 Forward Prediction,
13.4.2 Synthesis/Analysis Coding,
13.5 Block Coding,
13.5.1 Vector Quantizing,
13.6 Transform Coding,
13.6.1 Quantization for Transform Coding,
13.6.2 Subband Coding,
13.7 Source Coding for Digital Data,
13.7.1 Properties of Codes,
13.7.2 Huffman Codes,
13.7.3 Run-Length Codes,
13.8 Examples of Source Coding,
13.8.1 Audio Compression,
13.8.2 Image Compression,
13.9 Conclusion,
14 ENCRYPTION AND DECRYPTION 
14.1 Models, Goals, and Early Cipher Systems,
14.1.1 A Model of the Encryption and Decryption Process,
14.1.2 System Goals,
14.1.3 Classic Threats,
14.1.4 Classic Ciphers,
14.2 The Secrecy of a Cipher System,
14.2.1 Perfect Secrecy,
14.2.2 Entropy and Equivocation,
14.2.3 Rate of a Language and Redundancy,
14.2.4 Unicity Distance and Ideal Secrecy,
14.3 Practical Security,
14.3.1 Confusion and Diffusion,
14.3.2 Substitution,
14.3.3 Permutation,
14.3.4 Product Cipher Systems,
14.3.5 The Data Encryption Standard,
14.4 Stream Encryption,
14.4.1 Example of Key Generation Using a Linear
Feedback Shift Register,
14.4.2 Vulnerabilities of Linear Feedback Shift Registers,
14.4.3 Synchronous and Self-Synchronous Stream
Encryption Systems,
14.5 Public Key Cryptosystems,
14.5.1 Signature Authentication using a Public Key Cryptosystem,
14.5.2 A Trapdoor One-Way Function,
14.5.3 The Rivest-Shamir-Adelman Scheme,
14.5.4 The Knapsack Problem,
14.5.5 A Public Key Cryptosystem based on a Trapdoor Knapsack,
14.6 Pretty Good Privacy,
14.6.1 Triple-DBS, CAST, and IDEA,
14.6.2 Diffie-Hellman (Elgamal Variation) and RSA,
14.6.3 PGP Message Encryption,
14.6.4 PGP Authentication and Signature,
14.7 Conclusion,
15 FADING CHANNELS 
15.1 The Challenge of Communicating over Fading Channels,
15.2 Characterizing Mobile-Radio Propagation,
75.2.7 Large-Scale Fading,
15.2.2 Small-Scale Fading,
15.3 Signal Time-Spreading,
75.3.7 Signal Time-Spreading Viewed in the Time-Delay Domain,
15.3.2 Signal Time-Spreading Viewed in the Frequency Domain,
15.3.3 Examples of Flat Fading and Frequency-Selective Fading,
15.4 Time Variance of the Channel Caused by Motion,
75.4.7 Time Variance Viewed in the Time Domain,
15.4.2 Time Variance Viewed in the Doppler-Shift Domain,
15.4.3 Performance over a Slow-and Flat-Fading Rayleigh Channel,
15.5 Mitigating the Degradation Effects of Fading,
75.5.7 Mitigation to Combat Frequency-Selective Distortion,
75.5.2 Mitigation to Combat Fast-Fading Distortion,
15.5.3 Mitigation to Combat Loss in SNR,
15.5.4 Diversity Techniques,
15.5.5 Modulation Types for Fading Channels,
15.5.6 The Role of an Interleaver,
15.6 Summary of the Key Parameters Characterizing Fading Channels,
75.6.7 Fast Fading Distortion: Case 1,
15.6.2 Frequency-Selective Fading Distortion: Case 2,
15.6.3 Fast-Fading and Frequency-Selective Fading Distortion: Case 3,
15.7 Applications: Mitigating the Effects of Frequency-Selective Fading,
75.7.7 The Viterbi Equalizer as Applied to GSM,
15.7.2 The Rake Receiver as Applied to Direct-Sequence
Spread-Spectrum (DS/SS) Systems,
15.8 Conclusion,
A A REVIEW OF FOURIER TECHNIQUES
A.I Signals, Spectra, and Linear Systems,
A.2 Fourier Techniques for Linear System Analysis,
A2.7 Fourier Series Transform,
A.2.2 Spectrum of a Pulse Train,
A.2.3 Fourier Integral Transform,
A.3 Fourier Transform Properties,
A.3.1 Time Shifting Property,
A.3.2 Frequency Shifting Property,
A.4 Useful Functions,
A.4.1 Unit Impulse Function,
A.4.2 Spectrum of a Sinusoid
A.5 Convolution,
A5.7 Graphical Example of Convolution,
A.5.2 Time Convolution Property,
A.5.3 Frequency Convolution Property,
A.5.4 Convolution of a Function with a Unit Impulse,
A.5.5 Demodulation Application of Convolution,
A.6 Tables of Fourier Transforms and Operations,
B FUNDAMENTALS OF STATISTICAL DECISION THEORY 
B.I Bayes' Theorem,
5.7.7 Discrete Form of Bayes'Theorem,
B.1.2 Mixed Form of Bayes'Theorem,
B.2 Decision Theory,
5.2.7 Components of the Decision Theory Problem,
B.2.2 The Likelihood Ratio Test and the Maximum
A Posteriori Criterion,
B.2.3 The Maximum Likelihood Criterion,
B.3 Signal Detection Example,
B.3.1 The Maximum Likelihood Binary Decision,
B.3.2 Probability of Bit Error,
C RESPONSE OF A CORRELATOR TO WHITE NOISE 
D OFTEN-USED IDENTITIES 
E s-DOMAIN, z-DOMAIN AND DIGITAL FILTERING 
E.I The Laplace Transform,
£.7.7 Standard Laplace Transforms,
E.1.2 Laplace Transform Properties,
E.1.3 Using the Laplace Transform,
E.1.4 Transfer Function,
E.1.5 RC Circuit Low Pass Filtering,
E.1.6 Poles and Zeroes,
E.1.7 Linear System Stability,
E.2 The z-Transform,
E.2.1 Calculating the z-Transform,
E.2.2 The Inverse z-Transform,
E.3 Digital Filtering,
E.3.1 Digital Filter Transfer Function,
E.3.2 Single Pole Filter Stability,
E.3.3 General Digital Filter Stability,
E.3.4 z-Plane Pole-Zero Diagram and the Unit Circle,
£.3.5 Discrete Fourier Transform of Digital Filter Impulse Response,
E.4 Finite Impulse Response Filter Design,
E.4.1 FIR Filter Design,
E.4.2 The FIR Differentiator,
E.5 Infinite Impulse Response Filter Design,
E.5.1 Backward Difference Operator,
£.5.2 HR Filter Design using the Bilinear Transform,
E.5.3 The IIR Integrator,
F LIST OF SYMBOLS
INDEX