The theory and design of recombination nonuniform filter-banks with linear-phase analysis/synthesis filters

The 47th Midwest Symposium on Circuits and Systems Conference, Salt Lake City, Utah, USA, 25-28 July 2004This paper studies the theory and design of a class of linear-phase (LP) nonuniform filter-banks (FBs) called recombination nonuniform FBs (RNFBs). It is based on a recombination structure, where certain channels of an M-channel uniform FB are merged by synthesis filters of transmultiplexor (TMUX). It is assumed that the numbers of channels of the FB and TMUX are coprime to each other so that it is possible to obtain linear-time invariant (LTI) analysis/synthesis filters, instead of linear periodic time varying (LPTV) filters. The spectral supports of the analysis filters are analyzed, and the existence and matching conditions to obtain LP RNFBs with good frequency characteristics are then derived. The LTI representation of the analysis filters and the use of cosine-roll-off characteristics allow us to design the analysis filters by the REMEZ exchange algorithm. Design examples of LP nearly perfect reconstruction (NPR) RNFBs are given to demonstrate the effectiveness of the proposed method.published_or_final_versio

A new method for designing linear-phase recombination nonuniform filter-banks

The 47th Midwest Symposium on Circuits and Systems Conference, Salt Lake City, Utah, USA, 25-28 July 2004This paper proposes a new design method of linear-phase (LP) recombination nonuniform filter-banks (RNFBs), where certain channels of a uniform filter-bank (FB) are merged by sets of transmultiplexers (TMUXs). The case where the numbers of channels of the uniform FB and the TMUXs are not coprime to each other is studied in detail. By analyzing the spectrum supports of the analysis filters, it is found that the uniform FB and recombination TMUXs in the LP RNFBs can be designed separately as long as certain conditions are satisfied. This significantly simplifies the design procedure. Using this result, the design of a class of nearly PR LP RNFBs with cosine roll-off transition band based on the REMEZ algorithm is studied. Design examples show that LP RNFBs with good frequency responses and reasonably low reconstruction error can be obtained readily by the proposed method.published_or_final_versio

A rational subdivision scheme using cosine-modulated wavelets

This paper proposes a rational subdivision scheme using cosine-modulated wavelets. Subdivision schemes constructed from iterated filter banks can be used to generate wavelets and limit functions for multiresolution analysis. The proposed subdivision scheme is based on a kind of nonuniform filter banks called recombination nonuniform filterbanks (RN FB). It is shown that if the component FBs in a RNFB are wavelet FBs, then the necessary condition for convergence to limit functions in the subdivision scheme is also satisfied. Therefore, the design of different rational subdivision schemes is considerably simplified. An efficient RNFB, called RN cosine modulated FBs (CMFB), constructed from uniform CMFBs and cosinemodulated transmultiplexers (TMUX) are further investigated. Using a design technique for designing RN CMFB and cosine modulated wavelets (CMW) previously reported by the authors, very smooth limit functions can be generated from the rational subdivision scheme. A design example is given to illustrate the proposed method.published_or_final_versio

Theory and design of a class of cosine-modulated non-uniform filter banks

In this paper, the theory and design of a class of PR cosine-modulated nonuniform filter bank is proposed. It is based on a structure previously proposed by Cox, where the outputs of a uniform filter bank is combined or merged by means of the synthesis section of another filter bank with smaller channel number. Simplifications are imposed on this structure so that the design procedure can be considerably simplified. Due to the use of CMFB as the original and recombination filter banks, excellent filter quality and low design and implementation complexities can be achieved. Problems with these merging techniques such as spectrum inversion, equivalent filter representations and protrusion cancellation are also addressed. As the merging is performed after the decimation, the arithmetic complexity is lower than other conventional approaches. Design examples show that PR nonuniform filter banks with high stopband attenuation and low design and implementation complexities can be obtained by the proposed method.published_or_final_versio

A class of biorthogonal nonuniform cosine-modulated filter bankswith lower system delay

In this paper, the theory and design of a class of perfect-reconstruction (PR) biorthogonal nonuniform cosine-modulated filter banks (CMFB) is proposed. It is based on a recombination or merging structure previously proposed by the authors [1]. By relaxing the original CMFB and the recombination transmultiplexer (TMUX) to be biorthogonal, nonuniform CMFBs with lower system delay can be obtained. This increases the possible choices of the prototype filters and greatly reduces the overall system delay of the nonuniform filter bank. A new method is also introduced to suppress the spurious response resulting from the mismatch in the transition bands of the two biorthogonal CMFBs. Design example shows that nonuniform CMFBs with good stopband attenuation, lower system delay and implementation complexity can be realized using the proposed method.published_or_final_versio

A Novel Method for Designing M-Band Linear-Phase Perfrect-Reconstruction filter Banks

This paper studies the design of M-channel perfect-reconstruction (PR) linear-phase (LP) filter banks (FBs) with M=2k using a tree-structured FB. It is based on a observation of Fliege(1995) that the length of the analysis filters is decreased by a factor of two when the depth of the tree is increased by one, while its transition bandwidth is increased by the same factor. A lattice-based 2-channel LP FB is chosen because the frequency responses of the lowpass and highpass analysis (synthesis) filters can be designed to be closely symmetric to the other around π/2. By properly selecting the filter length, transition bandwidth. and stopband attenuation of the 2-channel PR LP FBs at each level of the tree structure, it is possible to design uniform PR LP FB with excellent frequency characteristic and much lower system delay.published_or_final_versio

Effective modulus of polycrystalline aggregates in different geometrical configurations

In the present study, a finite element scheme with random distribution strategy is employed to systematically investigate the modulus difference of polycrystalline copper aggregates in different geometrical configurations (three-dimensional bulk and thin film configurations). Firstly, the finite element simulation is performed to estimate the effective elastic constants in three-dimensional bulk configuration. The numerical estimations are in good agreement with the existing analytical solutions and experimental measurements. Secondly, the proven finite element scheme is extended to the prediction of the effective moduli of the free-standing and substrate-attached thin films. For the free-standing thin film, the effective Young's modulus decreases with reducing the film thickness. For the substrate-attached thin film, its effective modulus is affected by the relative stiffness between the substrate and the film. The spread of the effective moduli in different configurations could be as large as 20%. © 2010 Elsevier B.V.postprin

Growth of SiO x nanowire bunches cocatalyzed with Ga and Ni

Si Ox nanowire bunches were fabricated on Ni (N O3) 2* 6 H2 O solution-coated Si(111) substrates in a chemical vapor deposition system in the presence of Ga and under the flow of Ar and N H3 gases. The roles of nickel nitrate hydrate, gallium, and ammonia in the formation of Si Ox nanowire bunches were investigated. It was found that Ni and Ga act as catalysts for the growth, while nickel nitrate hydrate also serves as a source of oxygen. The growth mechanisms of different nanowire structures obtained by varying the fabrication conditions are discussed. © 2005 American Institute of Physics.published_or_final_versio

On the theory and design of a class of recombination nonuniform filter banks with low-delay FIR and IIR filters

This paper studies the theory and design of a class of recombination nonuniform FBs (RNFB) with low-delay (LD) FIR and IIR filters. The conditions for suppressing the spurious response and achieving a good frequency characteristic for these LD FIR/IIR RNFBs are developed. The proposed LD FIR RNFBs have a lower system delay than their linear-phase counterparts, at the expense of slight increase in phase distortion of the analysis filters and arithmetic complexity. By model reducing the LD FIR uniform FBs by the modified model reduction method, an IIR RNFB with a similar characteristic can be readily obtained. A design example is given illustrate the effectiveness of the proposed method. © 2006 IEEE.published_or_final_versio

On the theory and design of a class of PR uniform and recombination nonuniform causal-Stable IIR cosine modulated filter banks

This paper studies the theory and design of a class of perfect reconstruction (PR) uniform causal-stable infinite-impulse response (IIR) cosine modulated filter banks (CMFBs). The design approach is also applicable to the design of PR recombination nonuniform (RN) IIR CMFBs. The polyphase components of the prototype filters of these IIR CMFBs are assumed to have the same denominator so as to simplify the PR condition. In designing the proposed IIR CMFB, a PR FIR CMFB with similar specifications is first designed. The finite-impulse response prototype filter is then converted to a nearly PR (NPR) IIR CMFB using a modified model reduction technique. The NPR IIR CMFB so obtained has a reasonably low reconstruction error. Its denominator is designed to be a polynomial in z M, where M is the number of channels, to simplify the PR condition. Finally, it is employed as the initial guess to constrained nonlinear optimization software for the design of the PR IIR CMFB. Design results show that both NPR and PR IIR CMFBs with good frequency characteristics and different system delays can be obtained by the proposed method. By using these IIR CMFBs in the RN CMFBs, new RN NPR and PR IIR CMFBs can be obtained similarly. © 2008 IEEE.published_or_final_versio