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Topic: Nx2N lapped orthogonal transform
Replies: 13   Last Post: Sep 12, 2013 7:38 PM

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James Dow Allen

Posts: 15
Registered: 12/14/08
Nx2N lapped orthogonal transform
Posted: Aug 19, 2013 12:34 AM
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Let
( A B 0 )
( 0 A B )
( B 0 A )
be a 3Nx3N real matrix with A,B,0 each NxN and 0 an all-zeros matrix.

What is the necessary and sufficient condition for that matrix to be
orthogonal, i.e. that its transpose also be its inverse?

This problem statement can be considered ambiguous.
*But if you derive a good parametric form for (A B) you will know it.*

(I already "know the answer." I post from curiosity: Is this a VERY easy
problem, or just an easy problem.)

The problem does have some historic interest. Such transforms were in
vogue, briefly(?), in the 1990's for signal compression. A certain
Computer Sci. Professor published several papers and even a full-length
textbook on Nx2N lapped orthogonal transforms, with numerous Remarks and
Theorems which would all have been trivial Corollaries had he solved the
problem posed above.

James Dow Allen



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