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Topic: exp( m L + n K )
Replies: 0

 James "Jasha" Droppo Posts: 2 Registered: 12/12/04
exp( m L + n K )
Posted: Dec 6, 1996 11:04 PM

I have a problem that has come up in my research of discrete
time-frequency distributions. Perhaps someone can help. The problem is
analyzing the following matrix-valued function of two scalars:

A[m,n] = exp( 2j pi ( m L + n K ) / N ).

where m,n are integers
L is NxN, real and diagonal
K = F'L F (note: prime is Hermetian adjoint)
F is NxN Fourier matrix, (a,b) element is exp(2j pi a b/N)/sqrt(N)
F is Hermetian, normal, unitary, etc.

When m=0, this is obviously periodic in n, and when n=0, it is
periodic in m. Right now, I am computing this function using the
eigenvalue decomposition of mL + nK, but there must be a better
way...

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James 'Jasha' Garnet Droppo III jdroppo@u.washington.edu
Interactive Systems Design Lab
Department of Electrical Engineering ISDL: (206)543-7298
University of Washington
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James 'Jasha' Garnet Droppo III jdroppo@u.washington.edu
Interactive Systems Design Lab
Department of Electrical Engineering ISDL: (206)543-7298
University of Washington
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