Design of non-uniform filter banks-quadratic optimization with linear constraints

This paper presents methods for the design of non-uniform filter banks. The filter bank structure is obtained from a uniformly modulated filter bank by using an allpass transform which has a lossless frequency function and a nonlinear phase function. The proposed design method includes quadratic optimization with linear constraints. Considered applications are subband adaptive filtering and subband coding. Analysis filter banks and synthesis filter banks are designed in two subsequent stages, and design objectives include minimization of subband aliasing as well as reconstruction output residual aliasing components on an individual basis. This way to formulate design objectives is appropriate for filter banks used in subband adaptive filtering. Other design objectives are to optimize the overall filter bank response for low amplitude and phase distortion. Designs with phase compensation for linear phase overall response are included. Examples are included of filter banks with increasing bandwidth.