The example in Figure 1
illustrates a **pitfall** of classical inversion theory.
Had not overlapped **bold**s,
the crosstalk would have been removed perfectly.
We were not interested in destroying with ,and vice versa.
This result was just an accidental consequence of their overlap,
which came to dominate the analysis
because of the squaring in least squares.
Our failure could be attributed to a tacit assumption
that since and are somehow ``independent,''
they can be regarded as *orthogonal,* i.e., that .But the (potential) physical independence of and does nothing to make a short sample
of and orthogonal.
Even vectors containing random numbers are unlikely to be orthogonal
unless the vectors have an infinite number of components.
Perhaps if the text were as long
as the works of Shakespeare . . . .

10/21/1998