Interpolating filter banks in arbitrary dimensions

Details Interpolating filter banks in arbitrary dimensions Interpolating filter banks in arbitrary dimensions

2005-03-08

2005-03-08

Ngo, Chuong Dinh (Department: 2124)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

06865587

ABSTRACT:
Interpolating filter banks are constructed for use with signals which may be represented as a lattice of arbitrary dimension d. The filter banks include M channels, where M is greater than or equal to two. A given filter bank is built by first computing a set of shifts τias D−1ti, i=1, 2, . . . M−1, where tiis a set of coset representatives taken from a unit cell of the input signal lattice, and D is a dilation matrix having a determinant equal to M. A polynomial interpolation algorithm is then applied to determine weights for a set of M−1 predict filters Pihaving the shifts τi. A corresponding set of update filters Uiare then selected as Ui=P*i/M, where P*iis the adjoint of the predict filter Pi. The resulting predict and update filters are arranged in a lifting structure such that each of the predict and update filters are associated with a pair of the M channels of the filter bank. The input signal applied to the filter bank is downsampled in each of the M channels, and then interpolated using the M−1 predict filters and the M−1 update filters. The downsampled and interpolated signal may be reconstructed using complementary interpolation and upsampling operations.

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