Transmission of Information by Orthogonal Functions

by Henning F. Harmuth

Overview

The orthogonality of functions has been exploited in communications since its very beginning. Conscious and extensive use was made of it by KOTEL' NIKOV in theoretical work in 1947. Ten years later a considerable number of people were working in this field rather independently. However, little experimental use could be made of the theo- retical results before the arrival of solid state opera- tional amplifiers and integrated circuits. A theory of communication based on orthogonal functions could have been published many years ago. However, the only useful examples of orthogonal functions at that time were sine-cosine functions and block pulses, and this made the theory appear to be a complicated way to derive known re- sults. It was again the advance of semiconductor techno- logy that produced the first really new, useful example of orthogonal functions: the little-known Walsh functions. In this book emphasis is placed on the Walsh functions, since ample literature is available on sine-cosine func- tions as well as on block pulses and pulses derived from them.

Product Details

ISBN-13:	9783642533594
Publisher:	Springer Berlin Heidelberg
Publication date:	01/01/1970
Edition description:	Softcover reprint of the original 1st ed. 1970
Pages:	325
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

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 Auorrelation Function.- 5.Application of Orthogonal Functions to Statistical Problems.- 5.1 Series Expansion of Shastic 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.