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Xiqi Gao - One of the best experts on this subject based on the ideXlab platform.

  • theory and lattice structure of complex paraunitary filterbanks with filters of hermitian symmetry antisymmetry properties
    IEEE Transactions on Signal Processing, 2001
    Co-Authors: Xiqi Gao, T Q Nguyen, Gilbert Strang
    Abstract:

    The theory of the real-coefficient Linear-Phase filterbank (LPFB) is extended to the complex case in two ways, leading to two generalized classes of M-channel filterbanks. One is the symmetric/antisymmetric filterbank (SAFB), where all filters are symmetric or antisymmetric. The other is the complex Linear Phase filterbank (CLPFB), where all filters are Hermitian symmetric or Hermitian antisymmetric and, hence, have the Linear-Phase Property. Necessary conditions on the filter symmetry polarity and lengths for the existence of permissible solutions are investigated. Complete and minimal lattice structures are developed for the paraunitary SAFB and paraunitary CLPFB, where the channel number M is arbitrary (even or odd), and the subband filters could have different lengths. With the elementary unitary matrices in the structure of the paraunitary SAFB constrained to be real and orthogonal, the structure covers the most general real-coefficient paraunitary LPFBs. Compared with the existing results, the number of parameters is reduced significantly.

  • the theory and implementation of arbitrary length Linear Phase cosine modulated filter bank
    Signal Processing, 2000
    Co-Authors: Xiqi Gao, Xianggen Xia
    Abstract:

    Abstract In this paper, we propose an arbitrary-length Linear-Phase cosine-modulated filter bank (CMFB). It can be considered as an extension of the existing Linear-Phase CMFBs to arbitrary length. It is shown that the 2 M -channel arbitrary-length Linear-Phase CMFB needs to satisfy the same conditions as the conventional M -channel arbitrary-length CMFB does for perfect reconstruction. By using the Linear-Phase Property of a prototype filter, we obtain an efficient implementation structure in which 2×2 lossless lattices are used instead of 2×1 ones in the traditional implementation of the existing Linear-Phase CMFBs. The total number of the lattices is reduced by half.

Xianggen Xia - One of the best experts on this subject based on the ideXlab platform.

  • the theory and implementation of arbitrary length Linear Phase cosine modulated filter bank
    Signal Processing, 2000
    Co-Authors: Xiqi Gao, Xianggen Xia
    Abstract:

    Abstract In this paper, we propose an arbitrary-length Linear-Phase cosine-modulated filter bank (CMFB). It can be considered as an extension of the existing Linear-Phase CMFBs to arbitrary length. It is shown that the 2 M -channel arbitrary-length Linear-Phase CMFB needs to satisfy the same conditions as the conventional M -channel arbitrary-length CMFB does for perfect reconstruction. By using the Linear-Phase Property of a prototype filter, we obtain an efficient implementation structure in which 2×2 lossless lattices are used instead of 2×1 ones in the traditional implementation of the existing Linear-Phase CMFBs. The total number of the lattices is reduced by half.

Wayne Lawton - One of the best experts on this subject based on the ideXlab platform.

  • applications of complex valued wavelet transforms to subband decomposition
    IEEE Transactions on Signal Processing, 1993
    Co-Authors: Wayne Lawton
    Abstract:

    A method for constructing complex valued Linear Phase FIR conjugate quadrature filters and associated wavelet bases is described. Each filter is derived by replating certain zeros of a real valued FIR conjugate quadrature filter by their reciprocal conjugates. The derived filters have the same frequency response magnitudes as the original filters and their Linear Phase Property permits the use of symmetrization in subband decomposition to avoid border discontinuities that result from signal periodization. Subband decomposition and reconstruction using both a length 6 filter associated with a Daubechies (1988) wavelet bases and a related length 6 complex valued Linear Phase filter are compared to illustrate the reduced border effects. >

Valery A Zheludev - One of the best experts on this subject based on the ideXlab platform.

  • butterworth wavelet transforms derived from discrete interpolatory splines recursive implementation
    Signal Processing, 2001
    Co-Authors: Amir Averbuch, Alexander B Pevnyi, Valery A Zheludev
    Abstract:

    Abstract In the paper we present a new family of biorthogonal wavelet transforms and the related library of biorthogonal symmetric waveforms. For the construction we used the interpolatory discrete splines which enabled us to design a library of perfect reconstruction filter banks. These filter banks are related to Butterworth filters. The construction is performed in a “lifting” manner. The difference from the conventional lifting scheme is that the transforms of a signal are performed via recursive filtering with the use of IIR filters. These filters have Linear Phase Property and the basic waveforms are symmetric. The filters allow fast cascade or parallel implementation. We present explicit formulas for construction of wavelets with arbitrary number of vanishing moments. In addition, these filters yield perfect frequency resolution. The proposed scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature formulas.

Xuemei Xie - One of the best experts on this subject based on the ideXlab platform.

  • design of perfect reconstruction nonuniform filter banks with Linear Phase Property
    European Signal Processing Conference, 2009
    Co-Authors: Xuemei Xie, S C Chan
    Abstract:

    This paper proposes a new method for designing nonuniform filter banks (NUFBs) with perfect-reconstruction (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) are combined by the synthesis bank of recombination FBs. New matching conditions on the original and recombination FBs for the PR NUFBs to possess good frequency characteristics are derived. This simplifies the design of the PR LP RNUFBs to those of a set of appropriate PR LP uniform FBs, which greatly reduce the design complexity. The effectiveness of the proposed method is illustrated by the design of several PR LP RNUFBs with sampling factors (2/3, 1/3) and (1/3, 2/31).

  • a simple method for designing 2d imi channel near pr filter banks with Linear Phase Property
    Lecture Notes in Computer Science, 2006
    Co-Authors: Guangming Shi, Xuemei Xie, Liang Song, Danhua Liu
    Abstract:

    Two dimensional (2D) nonseparable filter banks with Linear Phase (LP) are desired for image sub-band coding and compression. In this paper, we propose a method for designing 2D nonseparable filter banks with the LP and near perfect reconstruction (near-PR) properties. By combining the unimodular transformation and a separable IMI-channel LP filter bank, the design problem is simplified to that of two one-dimensional (ID) LP filter banks. For 1D case, a novel method by employing partial cosine modulation is used to design near-PR filter banks with LP analysis and synthesis filters. For 2D case, we cascade two 1D near-PR LP filter banks in the form of tree structure to design a separable LP filter bank. With the unimodular transformation, a nonseparable LP filter bank is obtained. In addition, the filter bank achieves the near-PR Property without sophisticated nonLinear optimization procedures. Design example shows the efficiency and simplicity of the proposed method.