Signal/Vector Reconstruction from Projections
We now arrive finally at the main desired result for this section:
Theorem: The projections of any vector
onto any orthogonal basis set
for
can be summed to reconstruct
exactly.
Proof: Let
denote any orthogonal basis set for
.
Then since
is in the space spanned by these vectors, we have
for some (unique) scalars







![$\displaystyle {\bf P}_{\sv_k}(\sv_l) \isdef
\frac{\left<\sv_l,\sv_k\right>}{\l...
...ll}
\underline{0}, & l\neq k \\ [5pt]
\sv_k, & l=k. \\
\end{array} \right.
$](http://www.dsprelated.com/josimages_new/mdft/img973.png)








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