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Design methods for partial filter banks using interpolation

Two iterative algorithms for the design of partial filter banks using interpolation are described. The design problems are formulated as a 4th-order nonlinear optimization problems in which the objective function is a weighted sum of a reconstruction-error term and an aliasing-error term. The optimization problem is solved by iteratively minimizing a pair of quadratic functions. Explicit formulas for evaluating the minimums of these quadratic functions are described, which lead to an efficient and fast algorithm. Two design examples are presented to illustrate the proposed algorithms. The designed partial filter banks are used to approximate bathymetric waveforms and electrocardiagrams (ECGs).