Transmission of Information by Orthogonal Functions
Published on 6. December 2012
XI, 325 pages
978-3-642-53400-3 (ISBN)
Description
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.
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Henning F. Harmuth
Transmission of Information by Orthogonal Functions
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12/2012
2nd Edition
Springer
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Henning F. Harmuth
Transmission of Information by Orthogonal Functions
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01/1970
Springer
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Content
1.Mathematical Foundations.- 1.1 Orthogonal 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.- 2. Direct Transmission of Signals.- 2.1 Orthogonal Division as Generalization of Time and Frequency Division.- 2.2 Characterization of Communication Channels.- 2.3 Sequency Filters Based on Walsh Functions.- 3. Carrier Transmission of Signals.- 3.1 Amplitude Modulation(AM).- 3.2 Time Base, Time Position and Code Modulation.- 3.3 Nonsinusoidal Electromagnetic Waves.- 4. Statistical Variables.- 4.1 Single Variables.- 4.2 Combination of Variables.- 4.3 Statistical Dependence.- 5.Application of Orthogonal Functions to Statistical Problems.- 5.1 Series Expansion of Stochastic Functions.- 5.2 Additive Disturbances.- 5.3 Multiplicative Disturbances.- 6. Signal Design for Improved Reliability.- 6.1 Transmission Capacity.- 6.2 Error Probability of Signals.- 6.3 Coding.- References Ordered by Sections.- Additional References for the Second Printing.
