Polyphase structure-based approaches for FIR Mth-band filters and constrained filter banks : design, implementation and applications

TLDR: In this article, a generalized polyphase (GP) structure is proposed for the design of M th-band filters and filter banks, which is based on the polyphase matrix representation of the analysis and synthesis filters and a key idea of devising basic building blocks that are capable of propagating the desirable symmetry properties while being cascaded to generate the required lattice structures.

Abstract: Multirate systems, including M th-band filters and filter banks, have greatly facilitated the analysis, understanding and compression of signals. Polyphase structure plays an important role in the study of multirate systems due to the fact that it provides a parallel and very efficient implementation architecture. In this dissertation, some polyphase structure-based approaches for the design and implementation of M th-band filters as well as filter banks are presented. The emphasis is placed on the development of new structures that satisfy certain constraints and having low computational complexity. A design algorithm for M th-band filters is first presented based on the generalized polyphase (GP) structure. Both the interpolation and linear-phase conditions are incorporated in the proposed GP realization of M th-band filters. By deriving a closed-form frequency response specification for each of the constituent filters in the GP structure, the design of the original large-tap FIR filter is simplified to the design of short-length constituent filters to reduce the overall design complexity. The GP-based approach is then extended for the design of M th-band filters meeting certain regularity requirements. To show the wide applicability of the proposed method, the design of 2-D M th-band filters via the GP structure is also considered. It is shown that by applying the singular-value decomposition (SVD) to each 2-D subfilter in the GP structure, the implementation complexity of the overall 2-D filter can be significantly reduced without introducing a large error. The second part of the dissertation is concerned with the development of new lattice structures for perfect reconstruction filter banks (PRFBs) with certain constraints, such as the linear-phase (LP) and the minor-image symmetry (MIS). The innovative work is based on the polyphase matrix representation of the analysis and synthesis filters, and a key idea of devising basic building blocks that are capable of propagating the desirable symmetry properties while being cascaded to generate the required lattice structures. Due to the added constraints, the resulting lattice structures have fewer parameters, leading to a speedy optimization design and a reduction in the heavy implementation burden. It is proved that there exists a complete and minimal lattice structure for MIS-PRFBs. It is shown that a class of well-known filter banks, namely, the cosine-modulated filter banks (CMFBs), is a subclass of MIS-PRFBs, whose non-singular matrices are of sparse coefficients. By introducing more prototype filters, in conjunction with a proper modulation, new CMFBs with more parameters are generated. Combining the linear-phase and mirror-image symmetries, a lattice structure with further reduced number of parameters is also developed for MIS-LPPRFB. The designed MIS-LPPRFB is then utilized as a block transform for image compression coding. Simulation results show that the MIS-LPPRFB, despite its reduced number of parameters, offers a competitive performance in terms of both the visual quality and the peak signal-to-noise ratio for various images under a wide range of compression ratios