Design of perfect-reconstruction nonuniform recombination filter banks with flexible rational sampling factors

Abstract

This paper proposes a new method for designing nonuniform filter banks (NUFBs) with perfectreconstruction (PR) and linear-phase (LP) properties. It is based on the recombination structure, where the outputs of the analysis filters in a uniform original filter bank (FB) INTRODUCTIONThe theory and design of nonuniform filter banks (NUFBs) have received considerable attention due to their flexibility in subband partitioning and processing. In applications where phase distortion is an important concern, filter banks with linear-phase (LP) analysis and synthesis are highly desirable. For example, in image processing, LP filter banks (FBs) are frequently employed to avoid possible phase distortion. Among the various methods for designing NUFBs, only a few are applicable to the design of NUFBs satisfying the LP property [1][2][3], [6]. The tree-structure FB is a simple method for realizing PR LP NUFBs, but the choice of the decimation factors is usually limited and the system delay is rather long due to the cascade nature of the tree structure. Another class of design method is based on the direct structure in [1][2][3], where the analysis filters are designed directly [1] or by mean of iterative optimization algorithm. In channel number in order to generate subbands with different decimation factors. The advantage of the RNUFB is that the PR property is structurally imposed as long as the original uniform FB and the recombination FBs are PR. In [5,17] the theory and design of PR cosine-modulated RNUFBs are studied in detail. Due to large number of design variables and hence complexity associated with a general NUFB, even LP FBs are difficult to design in practice. The use of cosine modulatd FBs (CMFBs) greatly reduces the number of design variables and complexity. Consequently, high quality PR RNUFBs can be obtained. In [6], the design of linear phase RNUFBs is considered where a matching condition for orthogonal PR FBs was derived. However, due to the difficulties in designing LP original and recombination FBs with large number of channels, the RNUFBs so obtained are nearly PR.We note that the key difficulty in obtaining LP RNUFBs hinges on a design of the original and recombination PR LP FBs in the recombination structure. Among the existing methods for designing M-channel PR LP uniform FBs [7][8][9][10][11][12][13][14][15], the modulation-based approach is probably the simplest to apply [7][8][9]. However, the frequency support of these FBs is considerably different from that of uniform FBs. Therefore, it may not be suitable in RNUFBs. The lattice structure is another popular method for designing PR LP FBs, since the PR and linear phase property can be structural imposed [10][11][12][13][14]. Unfortunately, the frequency response becomes a very nonlinear function of a large number of lattice parameter, making the design very complicated and somewhat difficult to obtain good results as the filter length increases. In [15], a direct method for designing M-channel PR LP uniform FBs was proposed. By choosing...

Analysis of Signals via Non-Maximally Decimated Non-Uniform Filter Banks

“…were found to be equivalent to integer decimated NUFBs [16]. A number of design methods like direct method [15], recombination method [11], modulation based method [17], etc. exist in the literature.…”

Design of prototype filter using windowing and linear optimization technique for the non-uniform filter banks

“…Now a days, filter banks are used not compression but also found applications in [3] digital audio [4], heart beat detection in sub-band coding and the broad ban processing [13] . In these applications the n banks are very useful because it divides unequal bands.…”

“…One buildperfect reconstruction filter bank ev structure and the cascading filter banks are perfect reconstruction filter bank the filter u must be ideal which is unrealizable. There reconstruction (NPR) filter banks are practi In this paper, a prototype the windowing techniques and is optimized using the linear op ormation Technology (ICRTIT) owing and on-uniform cation, relaxed, at the cost of allowing l design methods [13,14] have of non-uniform filter bank using -optimization techniques. To ortion a linear optimization is no such iterative technique is e computational time and peak e, authors in [2] proposed a new the pass-band edge frequency linear optimization technique.…”

Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors

“…11 for Gröbner bases in general, and Refs. 1,7,20,25,26,28,32,33 for rational FB design). Using these methods, we are able to compute the shortest filters yielding orthonormal rational FBs with a number of vanishing moments.…”