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Full-Text Articles in Physical Sciences and Mathematics
Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen
Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen
SIUE Faculty Research, Scholarship, and Creative Activity
We give a number of explicit matrix-algorithms for analysis/synthesis
in multi-phase filtering; i.e., the operation on discrete-time signals which
allow a separation into frequency-band components, one for each of the
ranges of bands, say N , starting with low-pass, and then corresponding
filtering in the other band-ranges. If there are N bands, the individual
filters will be combined into a single matrix action; so a representation of
the combined operation on all N bands by an N x N matrix, where the
corresponding matrix-entries are periodic functions; or their extensions to
functions of a complex variable. Hence our setting entails …
Reproducing Kernel Hilbert Space Vs. Frame Estimates, Palle E. T. Jorgensen, Myung-Sin Song
Reproducing Kernel Hilbert Space Vs. Frame Estimates, Palle E. T. Jorgensen, Myung-Sin Song
SIUE Faculty Research, Scholarship, and Creative Activity
We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn Hinto a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gaussian processes.