Algorithms for computation are a central part of both digital
signal pro cessing and decoders for error-control codes and the
central algorithms of the two subjects share many similarities.
Each subject makes extensive use of the discrete Fourier transform,
of convolutions, and of algorithms for the inversion of Toeplitz
systems of equations. Digital signal processing is now an
established subject in its own right; it no longer needs to be
viewed as a digitized version of analog signal process ing.
Algebraic structures are becoming more important to its
development. Many of the techniques of digital signal processing
are valid in any algebraic field, although in most cases at least
part of the problem will naturally lie either in the real field or
the complex field because that is where the data originate. In
other cases the choice of field for computations may be up to the
algorithm designer, who usually chooses the real field or the
complex field because of familiarity with it or because it is
suitable for the particular application. Still, it is appropriate
to catalog the many algebraic fields in a way that is accessible to
students of digital signal processing, in hopes of stimulating new
applications to engineering tasks."
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