Cost reduced time varying fir filter

Details Cost reduced time varying fir filter Cost reduced time varying fir filter

1995-10-20

1998-02-10

Elmore, Reba I.

Boots, shoes, and leggings

364724011, G06F 1710

Patent

active

057176191

ABSTRACT:
A method and apparatus for computing, in real time, the coefficients C.sub..tau. (n) of a time varying FIR filter according to an optimum singular value decomposition (SVD) algorithm. The coefficients of a plurality of FIR filters are represented by a M.times.N matrix A.sub.M.times.N, where M is the number of FIR filters and N is the number of coefficients in the impulse response of each FIR filter (i.e., the number of filter taps). The A.sub.M.times.N matrix is factored into F.sub.M.times.N and G.sub.N.times.N matrices, and a singular value decomposition of the A.sub.M.times.N matrix is computed as A.sub.M.times.N =U.sub.M.times.N .cndot.D.sub.N.times.N .cndot.V.sub.N.times.N, where U.sub.M.times.N is a M.times.N unitary matrix, D.sub.N.times.N is a N.times.N diagonal matrix {.sigma..sub.1, .sigma..sub.2, . . . , .sigma..sub.N }, .sigma..sub.i are the singular values of A.sub.M.times.N (and .sigma..sub.1 .gtoreq..sigma..sub.2 . . . .gtoreq..sigma..sub.N .gtoreq.0), and V.sub.N.times.N is a N.times.N unitary matrix. By selecting a predetermined L number of the largest singular values .sigma. to generate a reduced size diagonal matrix D.sub.L.times.L, it is possible to extract the first L columns from the U.sub.M.times.N matrix to form a reduced U.sub.M.times.L matrix and to extract the first L rows from the V.sub.N.times.N matrix to form a reduced V.sub.L.times.N matrix. In this manner the filter matrix A.sub.M.times.N can be approximated by reducing the F.sub.M.times.N and G.sub.N.times.N matrices by replacing N with L such that:

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