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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 timefrequency distributions. Perhaps someone can help. The problem is analyzing the following matrixvalued 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...
 James 'Jasha' Garnet Droppo III jdroppo@u.washington.edu Interactive Systems Design Lab Department of Electrical Engineering ISDL: (206)5437298 University of Washington    James 'Jasha' Garnet Droppo III jdroppo@u.washington.edu Interactive Systems Design Lab Department of Electrical Engineering ISDL: (206)5437298 University of Washington 



