Digital Signal Processing Reference
In-Depth Information
where
Using superscript
for the deviation from
e.g.
the Taylor expansion can be rewritten by
2.2
Multiple regression of multi-channel signals
Approximation of
by the multiple-regression of
has the
form
By substituting equation (4), the regression error of the approxima-
tion,
can be calculated as follows.
Assuming the orthogonality between
and
the expec-
tation value of the regression error becomes
The minimum regression error is then achieved when
Thus, the optimal can be uniquely determined as a vector that is
orthogonal to and its inner product with is equal to unity. The
relationship among these three vectors are shown in Figure 19-2.
