Design Of Two-channel Filter Banks Research Articles

Filter Design for Two-Channel Filter Banks on Directed Bipartite Graphs

Graph signal processing on directed graphs is more challenging that on undirected graph, primarily because the graph matrices, e.g., adjacency or Laplacian, associated with the latter is non-symmetric. The eigenvalues that represent the spectral frequencies are therefore complex in general, and the design of spectral filters for complex frequencies presents more challenges. In this work we consider the design of two-channel filter banks for directed bipartite graphs. By decomposing any graph into a series of bipartite graphs, the basic two-channel system can be applied in cascade for arbitrary graphs. The graph filters are constructed using ladder structures. The design of the kernels in the ladder structures is achieved via a least-squares formulation. Analytical formulas are derived for the design of the kernel coefficients.

Structure and design of two-channel filter banks derived from a triplet of halfband filters

A novel approach for the construction of two-channel one-dimensional (1-D) biorthogonal filter banks is described. This approach is intended to help overcome limitations in an otherwise effective set of recently proposed techniques while retaining the advantages of a simple design and feature-rich structure. The novelty of the method rests on the use of a triplet of halfband fillers, which are combined in a convenient form of the transfer function with adjustable parameters that provide the necessary flexibility in obtaining the desired response. Design procedures are described for the construction of the filter banks by casting the approximation problem in a form that easily lends itself to Remez exchange algorithm. In these design procedures, the analysis and synthesis filters can be either finite-duration impulse response, infinite duration impulse response, or a hybrid. Examples of design of 1-D filter banks and extension of the technique to two-dimensional diamond filter banks are presented. Finally, subband image-coding examples are given to demonstrate the advantage of the proposed filter-bank structure.