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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

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

Date Subject Author
8/19/13 James Dow Allen
8/19/13 Nicolas Bonneel
8/20/13 Robin Chapman
8/20/13 Nicolas Bonneel
8/20/13 quasi
8/20/13 Nicolas Bonneel
8/20/13 Roland Franzius
8/20/13 James Dow Allen
9/3/13 James Dow Allen
9/3/13 Robin Chapman
9/3/13 Leon Aigret
9/5/13 James Dow Allen
9/5/13 Robin Chapman
9/12/13 Leon Aigret