基于拉格朗日乘子法的二维修正DFT调制滤波器组设计算法

周芳; 水鹏朗; 蒋俊正

doi:10.11999/JEIT160651

基于拉格朗日乘子法的二维修正DFT调制滤波器组设计算法

doi: 10.11999/JEIT160651

2.
(西安电子科技大学雷达信号处理国家重点实验室西安 710071) ②(桂林电子科技大学生命与环境科学学院桂林 541004) ③(桂林电子科技大学信息与通信学院桂林 541004)

基金项目:

国家自然科学基金(61261032)

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出版历程
- 收稿日期: 2016-06-21
- 修回日期: 2016-11-28
- 刊出日期: 2017-05-19

Design of Two-dimensional Modified DFT Modulated Filter Banks Based on Lagrange Multiplier Method

2.
(National Laboratory of Radar Signal Processing, Xidian University, Xi&rsquo

Funds:

The National Natural Science Foundation of China (61261032)

摘要

摘要: 基于拉格朗日乘子法，该文提出一种2维修正离散傅里叶变换调制滤波器组的迭代设计方法。在每次迭代中，原型滤波器的设计描述成一个约束为2次函数的2次规划问题。引入拉格朗日乘子法将问题转化为无约束的优化问题，通过求解线性矩阵方程得到优化问题的解。针对矩阵方程中的系数矩阵的特点，运用块LU分解，显著降低了运算复杂度。仿真实验表明，与现有的设计方法相比，该文方法设计得到的2维修正离散傅里叶变换调制滤波器组的重构误差和阻带衰减均有较大的改善。
- 2维修正滤波器组 /
- 离散傅里叶变换调制 /
- 迭代优化 /
- 拉格朗日乘子法 /
- 块LU分解
Abstract: Base on Lagrange multiplier method, an iterative algorithm is proposed to design the two-dimensional modified Discrete Fourier Transform (DFT) modulated filter bank. In each iteration, the design problem is described as a Quadratically Constrained Quadratic Program (QCQP). The Lagrange multiplier method is then employed to transform the constrained problem into an unconstrained one, the solution of which is obtained by solving a set of linear equations. By analyzing the coefficient matrix, block LU factorization is applied to considerably reduce the computational complexity. Numerical results and comparison with the existing methods demonstrate the improved performance of the proposed scheme, including the reconstruction error and stopband attenuation.
- Two-dimensional modified filter bank /
- DFT modulated /
- Iteration optimization /
- Lagrange multiplier method /
- Block LU factorization

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参考文献(19)

VAIDYANATHAN P P. Multirate Systems and Filter Banks[M]. Englewood Cliffs, NJ, US, Prentice-Hall, 1993: 545-650.

江淮, 赵惠昌, 汉敏, 等. 基于DFT滤波器组的大斜视SAR成像算法[J]. 电子与信息学报, 2016, 38(1): 104-110. doi: 10.11999/JEIT150381.

JIANG Huai, ZHAO Huichang, HAN Min, et al. Highly squint SAR imaging algorithm based on DFT filter banks[J]. Journal of Electronics Information Technology, 2016, 38(1): 104-110. doi: 10.11999/JEIT150381.

周祚峰, 曹剑中, 程源源, 等. 新的方向滤波器组及其在图像去噪中的应用[J]. 光子学报, 2010, 39(2), 380-384. doi: 10.3788/gzxb20103902.0380.

ZHOU Zuofeng, CAO Jianzhong, CHENG Yuanyuan, et al. New directional filter bank and its application in image denoising[J]. Acta Photonica Sinica, 2010, 39(2): 380-384. doi: 10.3788/gzxb20103902.0380.

SUZUKI T and KUDO H. Two-dimensional non-separable block-lifting structure and its application to M-channel perfect reconstruction filter banks for lossy-to-lossless image coding[J]. IEEE Transactions on Image Processing, 2015, 24(12): 4943-4951. doi: 10.1109/TIP.2015.2472294.

GAWANDE J P, RAHULKAR A D, and HOLAMBE R S. Design of new class of regular biorthogonal wavelet filter banks using generalized and hybrid lifting structures[J]. Signal Image and Video Processing, 2015, 9(1): 265-273. doi: 10.1007/s11760-015-0814-0.

蒋俊正, 程小磊, 欧阳缮. 双原型离散傅里叶变换调制滤波器组的快速设计方法[J]. 电子与信息学报, 2015, 37(11): 2628-2633. doi: 10.11999/JEIT150298.

JIANG Junzheng, CHENG Xiaolei, and OUYANG Shan. Fast design of double-prototype discrete fourier transform modulated filter banks[J]. Journal of Electronics Information Technology, 2015, 37(11): 2628-2633. doi: 10.11999/JEIT150298.

JIANG J Z, ZHOU F, SHUI P L, et al. Theory and design of two-dimensional DFT modulated filter bank with arbitrary modulation and decimation matrices[J]. Digital Signal Processing, 2015, 44(1): 123-130. doi: 10.1016/j.dsp.2015. 05.012.

JIANG J Z and SHUI P L. Design of 2D oversampled linear phase DFT modulated filter banks via modified Newton's method[J]. Signal Processing, 2012, 92(6): 1411-1421. doi: 10.1016/j.sigpro.2011.11.029.

ZHOU F, JIANG J Z, and SHUI P L. Fast design of 2D fully oversampled DFT modulated filter bank using Toeplitz-block Toeplitz matrix inversion[J]. Signal Processing, 2015, 111: 194-198. doi: 10.1016/j.sigpro.2014.12.021.

蒋俊正. DFT调制滤波器组的设计算法研究[D]. [博士学位论文], 西安电子科技大学, 2011: 81-106.

JIANG Junzheng. Design algorithms of DFT modulated filter banks[D]. [Ph.D. dissertation], Xidian University, 2011: 81-106.

SHUI P L and JIANG J Z. Two-dimensional 2 oversampled DFT modulated filter banks and critically sampled modified DFT modulated filter banks[J]. IEEE Transactions on Signal Processing, 2010, 58(11): 5597-5611. doi: 10.1109/TSP.2010. 2059016.

JIANG J Z and ZHOU F. Iterative design of two-dimensional critically sampled MDFT modulated filter banks[J]. Signal Processing, 2013, 93(11): 3124-3132. doi: 10.1016/j.sigpro. 2013.03.022.

ZHANG Z J and Yang Y. Efficient iterative design of modified DFT filter banks[J]. Electronics Letters, 2011, 47(15): 846-847. doi: 10.1049/el.2011.1450.

HIGHAM N J. Accuracy and Stability of Numerical Algorithms[M]. Philadelphia, PA, US, Society for Industrial and Applied Mathematics, 2002: 245-258.

LU W S, ANTONIOU A, and XU H. A direct method for the design of 2-D nonseparable filter banks[J]. IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, 1998, 45(8): 1146-1150. doi: 10.1109/82.718828.

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