Walsh Functions and Data Communication

Walsh functions are mathematical functions. They are presently the most important example of non-sinusoidal functions in communications. They are used in G1, G2, and G3 systems as well as in the GPS systems. Very little information is published about their military and commercial applications which are numerous. Furthermore, generally speaking very little information is published on Walsh functions, and specifically nothing on generating methods using electronic circuits, a topic which...
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Walsh functions are mathematical functions. They are presently the most important example of non-sinusoidal functions in communications. They are used in G1, G2, and G3 systems as well as in the GPS systems. Very little information is published about their military and commercial applications which are numerous. Furthermore, generally speaking very little information is published on Walsh functions, and specifically nothing on generating methods using electronic circuits, a topic which is very important to communication engineers and other scientists working in this field. The intention of writing this book is to compiles information covering a detailed mathematical theory of Walsh functions, some of their characteristics, their hardware implementation, and the development of a systematic method to electronically generate Walsh functions. Furthermore, the related communication subjects presented are added to the content of this book because of the importance of Walsh functions in the today's advanced communication technology. The topics on communication were presented in such a way that their basic principles and functions, as well as advantages and disadvantages are discussed. The book offers the reader basic understanding of Walsh functions as well as of communication systems. Chapter one presents detailed discussion on the basic theory of Walsh functions, their characteristics, and how they are generated mathematically as well as a step by step development of hardware circuit which systematically produces Walsh functions sequences. Military and other applications of Walsh functions are of grate importance however, another wide spread application is in the commercial communication field. Chapter two discusses topics of analog modulation such as; Amplitude Modulation (AM); Frequency Modulation (FM) and Phase Modulation (PM). In addition Digital Modulation techniques such as; Pulse Amplitude Modulation (PAM), Pulse Duration Modulation (PDM), Pulse Position Modulation (PPM) and Pulse Code Modulation (PCM) were discussed. Chapter three discusses topics of Analog Multiplexing and de-Multiplexing techniques like; Frequency Division Multiplexing (FDM), Wavelength Division Multiplexing (WDM), Time Division Multiplexing (TDM) and Code Division Multiplexing (CDM). Chapter four discusses an important mathematical tool which is very useful in the field of communication; namely Fourier series and Fourier integral. This chapter is added to the content of this book, because by applying Fourier series and integral one can determine bandwidth and harmonics contents of non-sinusoidal data signals. Fourier analysis is also used in sampling theorem.