Transmission of Information by Orthogonal Functions

1.Mathematical Foundations.- 1.1 Orthogonal Functions.- 1.11 Orthogonality and Linear Independence.- 1.12 Series Expansion by Orthogonal Functions.- 1.13 Invariance of Orthogonality to Fourier Transformation.- 1.14 Walsh Functions.- 1.2 The Fourier Transform and its Generalization.- 1.21 Transition from Fourier Series to Fourier Transform.- 1.22 Generalized Fourier Transform.- 1.23 Invariance of Orthogonality to the Generalized Fourier Transform.- 1.24 Examples of the Generalized Fourier Transform.- 1.25 Fast Walsh-Fourier Transform.- 1.26 Generalized Laplace Transform.- 1.3 Generalized Frequency.- 1.31 Physical Interpretation of the Generalized Frequency.- 1.32 Power Spectrum, Amplitude Spectrum, Filtering of Signals.- 1.33 Examples of Walsh Fourier Transforms and Power Spectra.- 2. Direct Transmission of Signals.- 2.1 Orthogonal Division as Generalization of Time and Frequency Division.- 2.11 Representation of Signals.- 2.12 Examples of Signals.- 2.13 Amplitude Sampling and Orthogonal Decomposition.- 2.14 Circuits for Orthogonal Division.- 2.15 Transmission of Digital Signals by Sine and Cosine Pulses.- 2.2 Characterization of Communication Channels.- 2.21 Frequency Response of Attenuation and Phase Shift of a Communication Channel.- 2.22 Characterization of a Communication Channel by Crosstalk Parameters.- 2.3 Sequency Filters Based on Walsh Functions.- 2.31 Sequency Lowpass Filters.- 2.32 Sequency Bandpass Filters.- 2.33 Digital Sequency Filters.- 3. Carrier Transmission of Signals.- 3.1 Amplitude Modulation(AM).- 3.11 Modulation and Synchronous Demodulation.- 3.12 Multiplex Systems.- 3.13 Digital Multiplexing.- 3.14 Methods of Single Sideband Modulation.- 3.15 Correction of Time Differences in Synchronous Demodulation.- 3.2 Time Base, Time Position and Code Modulation.- 3.21 Time Base Modulation (TBM).- 3.22 Time Position Modulation (TPM).- 3.23 Code Modulation (CM).- 3.3 Nonsinusoidal Electromagnetic Waves.- 3.31 Radiation of Walsh Waves by a Hertzian Dipole.- 3.32 Propagation, Antennas, Doppler Effect.- 3.33 Interferometry, Shape Recognition.- 4. Statistical Variables.- 4.1 Single Variables.- 4.11 Definitions.- 4.12 Density Function, Function of a Random Variable, Mathematical Expectation.- 4.13 Moments and Characteristic Function.- 4.2 Combination of Variables.- 4.21 Addition of Independent Variables.- 4.22 Joint Distributions of Independent Variables.- 4.3 Statistical Dependence.- 4.31 Covariance and Correlation.- 4.32 Cross- and Autocorrelation Function.- 5.Application of Orthogonal Functions to Statistical Problems.- 5.1 Series Expansion of Stochastic Functions.- 5.11 Thermal Noise.- 5.12 Statistical Independence of the Components of an Orthogonal Expansion.- 5.2 Additive Disturbances.- 5.21 Least Mean Square Deviation of a Signal from Sample Functions.- 5.22 Examples of Circuits.- 5.23 Matched Filters.- 5.24 Compandors for Sequency Signals.- 5.3 Multiplicative Disturbances.- 5.31 Interference Fading.- 5.32 Diversity Transmission Using Many Copies.- 6. Signal Design for Improved Reliability.- 6.1 Transmission Capacity.- 6.11 Measures of Bandwidth.- 6.12 Transmission Capacity of Communication Channels.- 6.13 Signal Delay and Signal Distortions.- 6.2 Error Probability of Signals.- 6.21 Error Probability of Simple Signals due to Thermal Noise.- 6.22 Peak Power Limited Signals.- 6.23 Pulse-Type Disturbances.- 6.3 Coding.- 6.31 Coding with Binary Elements.- 6.32 Orthogonal, Transorthogonal and Biorthogonal Alphabets.- 6.33 Coding for Error-Free Transmission.- 6.34 Ternary Combination Alphabets.- 6.35 Combination Alphabets of Order 2r+1.- References Ordered by Sections.- Additional References for the Second Printing.