A new design scheme of two-channel graph filter bank

Abstract

The existing designs of a two-channel graph filter bank (2c-graph-FB) are polynomial-based and have the numerical calculation problem when designing high performance/order 2c-graph-FB. In this study, a new design scheme is proposed to overcome the numerical calculation problem. The basic idea is adopting the expression form of the traditional symmetric finite impulse response (FIR) filter's frequency response as that of the frequency-domain graph filter of a 2c-graph-FB. Further, for solving the contradiction between the order and the vertex-domain localization in the existing designs as well as the proposed design, the idea of approximate vertex-domain localization is proposed. The designed 2c-graph-FB via our proposed scheme can have strict or approximate vertex-domain localization property. The simulation results reveal that the proposed scheme has no numerical calculation problem. Moreover, compared with the existing designs on the condition of all being able to achieve exceedingly small reconstruction error, the proposed design with the strict localization property has superior frequency selectivity. Among the existing designs (also including the proposed design with strict or approximate localization property) which can achieve exceedingly small reconstruction error, the proposed design scheme with the approximate localization property performs best in terms of the frequency selectivity while having certain localization property.