| 摘要 |
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 &tgr;i as D-1ti, i=1, 2, . . . M-1, where ti is 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 Pi having the shifts &tgr;i. A corresponding set of update filters Ui are then selected as Ui=Pi*|M, where Pi* is 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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