Design of oversampled double-prototype DFT modulated filter banks via bi-iterative second-order cone program

  • Authors:

  • Peng-Lang Shui;Jun-Zheng Jiang;Xiao-Long Wang

  • Affiliations:

  • National Laboratory of Radar Signal Processing, Xidian University, Xi'an, 710071, China;National Laboratory of Radar Signal Processing, Xidian University, Xi'an, 710071, China;National Laboratory of Radar Signal Processing, Xidian University, Xi'an, 710071, China

  • Venue:
  • Signal Processing
  • Year:
  • 2010

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Abstract

Oversampled double-prototype DFT modulated filter banks can achieve better overall performance than their single-prototype counterparts, owing to more degrees of freedom available in design. In this paper, we reformulate their design problem into a non-convex optimization, which minimizes the maximal amplitude of the transfer function distortion and aliasing transfer functions of the filter bank subject to fixed bounds on stopband and transition-band energy and the passband flatness of the prototype filters (PFs), and the inband aliasing of the analysis filters. A bi-iterative second-order cone program (BI-SOCP) algorithm is proposed to solve the non-convex optimization. The BI-SOCP can always generate filter banks with satisfactory overall performance starting from appropriate initial PFs, though the iteration process cannot assure to converge to the optimal solution of the problem. The new formulization allows the component cancellation of each aliasing transfer function. The BI-SOCP can still design filter banks of nearly perfect reconstruction (NPR) in the case of less redundancy ratio and short PFs. Finally, several numerical examples are demonstrated to verify the effectiveness of the algorithm.