二維雙原型完全過采樣DFT調(diào)制濾波器組的快速設(shè)計(jì)方法
doi: 10.11999/JEIT160125
基金項(xiàng)目:
國家自然科學(xué)基金(61261032, 61371186)，廣西區(qū)自然科學(xué)基金 (2013GXNSFBA019264)
Fast Design of 2D and Double-prototype Fully Oversampled DFT Modulated Filter Banks
Funds:
The National Natural Science Foundation of China (61261032, 61371186), The Guangxi Natural Science Foundation (2013GXNSFBA019264)
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摘要: 傳統(tǒng)的2維大規(guī)模濾波器組的設(shè)計(jì)方法具有復(fù)雜度高的缺點(diǎn)。該文提出一種設(shè)計(jì)2維雙原型濾波器組的快速方法，該方法利用近似完全重構(gòu)的條件，并采用完全過采樣的離散傅里葉變換(DFT)調(diào)制濾波器組來設(shè)計(jì)。新算法將兩個(gè)原型濾波器的設(shè)計(jì)問題歸結(jié)為一個(gè)無約束優(yōu)化問題，其中目標(biāo)函數(shù)為濾波器組的總體失真(傳遞失真和混疊失真)與原型濾波器阻帶能量的加權(quán)和，利用目標(biāo)函數(shù)的梯度向量，通過雙迭代機(jī)制求解該優(yōu)化問題。單步迭代中，利用矩陣求逆的等效條件和塊Toeplitz矩陣求逆的快速算法，顯著地降低了計(jì)算復(fù)雜度。理論分析和數(shù)值實(shí)驗(yàn)表明，新算法可以得到整體性能更好的濾波器組，計(jì)算復(fù)雜度大幅度降低，故可以快速設(shè)計(jì)大規(guī)模的2維濾波器組。
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關(guān)鍵詞:
- 2維離散傅里葉變換 /
- 無約束優(yōu)化 /
- 完全過采樣 /
- 塊Toeplitz矩陣求逆 /
- 雙迭代算法
Abstract: Traditional design methods of two-dimensional large-scale filter banks suffer from high-complexity. This paper presents an algorithm to design two-dimensional double-prototype fully oversampled Discrete Fourier Transform (DFT) modulated filter bank with Nearly Perfect Reconstruction (NPR). The algorithm is based on bi-iterative scheme, where the design issue is formulated into an unconstrained optimization issue whose objective function is the weighted sum of the transfer distortion and the aliasing distortion of the filter bank, and the stopband energy of the Prototype Filters (PFs). By exploiting the gradient information, the optimization problem can be efficiently solved by utilizing the bi-iterative scheme. The matrix inverse identity and the fast algorithm for Toeplitz-block Toeplitz matrix inversion are employed to dramatically reduce the computational cost of the iterative procedure. The theoretical analysis and numerical experiments are carried out to show that compared with the existing methods, the new algorithm possesses much lower computational cost and can be used to design large-scale two-dimensional filter bank with better overall performance. -
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