基于拉格朗日乘子法的二維修正DFT調(diào)制濾波器組設(shè)計算法

周芳; 水鵬朗; 蔣俊正

doi:10.11999/JEIT160651

基于拉格朗日乘子法的二維修正DFT調(diào)制濾波器組設(shè)計算法

doi: 10.11999/JEIT160651 cstr: 32379.14.JEIT160651

2.
(西安電子科技大學(xué)雷達信號處理國家重點實驗室西安 710071) ②(桂林電子科技大學(xué)生命與環(huán)境科學(xué)學(xué)院桂林 541004) ③(桂林電子科技大學(xué)信息與通信學(xué)院桂林 541004)

基金項目:

國家自然科學(xué)基金(61261032)

計量
- 文章訪問數(shù): 1293
- HTML全文瀏覽量: 214
- PDF下載量: 309
- 被引次數(shù): 0
出版歷程
- 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，該文提出一種2維修正離散傅里葉變換調(diào)制濾波器組的迭代設(shè)計方法。在每次迭代中，原型濾波器的設(shè)計描述成一個約束為2次函數(shù)的2次規(guī)劃問題。引入拉格朗日乘子法將問題轉(zhuǎn)化為無約束的優(yōu)化問題，通過求解線性矩陣方程得到優(yōu)化問題的解。針對矩陣方程中的系數(shù)矩陣的特點，運用塊LU分解，顯著降低了運算復(fù)雜度。仿真實驗表明，與現(xiàn)有的設(shè)計方法相比，該文方法設(shè)計得到的2維修正離散傅里葉變換調(diào)制濾波器組的重構(gòu)誤差和阻帶衰減均有較大的改善。
- 2維修正濾波器組 /
- 離散傅里葉變換調(diào)制 /
- 迭代優(yōu)化 /
- 拉格朗日乘子法 /
- 塊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

HTML全文

參考文獻(19)

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

江淮, 趙惠昌, 漢敏, 等. 基于DFT濾波器組的大斜視SAR成像算法[J]. 電子與信息學(xué)報, 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, 曹劍中, 程源源, 等. 新的方向濾波器組及其在圖像去噪中的應(yīng)用[J]. 光子學(xué)報, 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.

蔣俊正, 程小磊, 歐陽繕. 雙原型離散傅里葉變換調(diào)制濾波器組的快速設(shè)計方法[J]. 電子與信息學(xué)報, 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.

蔣俊正. DFT調(diào)制濾波器組的設(shè)計算法研究[D]. [博士學(xué)位論文], 西安電子科技大學(xué), 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.

相關(guān)文章

施引文獻

資源附件(0)

訪問統(tǒng)計