| The system of sine and cosine functions has been
distinguished historically in communications. Whenever the term frequency
is used, reference is made implicitly to these functions; hence the generally
used theory of communication is based on the system of sine and cosine
functions. In recent years other complete systems of orthogonal functions
have been used for theoretical investigations as well as for equipment
design. Analogs to Fourier series, Fourier transform, frequency, power
spectra, and amplitude, phase, and frequency modulation exist for many
systems of orthogonal functions. This implies that theories of communication
can be worked out on the basis of these systems. Most of these theories
are of academic interest only. However, for the complete system of the
orthogonal Walsh functions, the implementation of circuits by modern semiconductor
techniques appears to be competitive in a number of applications with the
implementation of circuits for the system of sine and cosine functions.
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