On The Study Of Nonuniform Filter Banks

Digital filter banks have been widely used in many applications, such as communications, radar, system identification, speech coding, and image signal processing, etc. Recently, a large amount of attention has been paid to the study of the nonuniform filter banks (NUFBs) due to their flexibility in partitioning subbands. This thesis mainly studies the theory and design of maximally decimated NUFBs.Firstly, we study the design methods and perfect-reconstruction (PR) conditions for NUFBs. We give the classification of the design methods in the literature, as well as their characteristics. For the PR necessary conditions, we summarize and extend the necessary conditions that the samplers of PR NUFBs must satisfy. Based on these analyses, the systematized test for the sampling factors is given. By the systematized test, we can quickly reject certain decimators from being considered to build PR NUFBs, and remain those which have the possibility to construct PR NUFBs. Note not all these remained decimators can realize the PR of NUFB, because the systematized test is based on the necessary condition for the PR NUFB, while the necessary and sufficient condition on decimator set is still an open problem.Secondly, we propose a method for designing NUFBs with PR and linear-phase (LP) properties. The method is based on the recombination structure, where the outputs of a uniform original filter bank (FB) are combined by synthesis section of a recombination FB. We deduce the matching conditions for the original and recombination FBs, which are necessary for the constructed PR NUFBs having good frequency responses. With those conditions being satisfied, the designing of PR LP NUFBs becomes that of a set of PR LP uniform FBs, reducing the design complexity.Finally, a novel method for signal decomposition and denoising is proposed based on the NUFB, which is derived from a uniform FB. With this method, the signal is firstly decomposed into M subbands using a uniform FB. Then according to their energy distribution, the corresponding consecutive filters are merged to compose the NUFB. With the resulting NUFB, the signal can be readily matched and flexibly decomposed according to its power spectrum distribution. Furthermore, this method can be used to detect and remove the narrow-band noise from the corrupted signal.