  In studying the unusual properties of a special Witt basis of a Clifford
geometric algebra with a Lorentz metric, a new concept of local duality makes
it possible to define any real geometric algebra by complexifying this
structure. Whereas a global basis of Witt null vectors is defined in terms of a
pair of correlated Grassmann algebras in a geometric algebra of neutral
signature, the special Witt basis of a Lorentz geometric algebra is defined in
terms of a single Grassmann algebra. The relationship between these different
concepts of duality, and their matrix representations, is studied in terms of
simple examples. A surprising connection is exhibited between discrete Fourier
and Wavelet transforms and the concept of local duality.
