雙原型離散傅里葉變換調(diào)制濾波器組的快速設(shè)計(jì)方法

蔣俊正; 程小磊; 歐陽繕

doi:10.11999/JEIT150298

雙原型離散傅里葉變換調(diào)制濾波器組的快速設(shè)計(jì)方法

doi: 10.11999/JEIT150298 cstr: 32379.14.JEIT150298

基金項(xiàng)目:

國家自然科學(xué)基金(61371186, 61261032)和廣西區(qū)自然科學(xué)基金(2013GXNSFBA019264)

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- 文章訪問數(shù): 1436
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- 被引次數(shù): 0
出版歷程
- 收稿日期: 2015-03-11
- 修回日期: 2015-07-13
- 刊出日期: 2015-11-19

Fast Design of Double-prototype Discrete Fourier Transform Modulated Filter Banks

Funds:

The National Natural Science Foundation of China (61261032)

摘要

摘要: 針對大規(guī)模的離散傅里葉變換(DFT)調(diào)制濾波器組設(shè)計(jì)算法復(fù)雜度高的問題，該文提出一種基于無約束優(yōu)化的快速設(shè)計(jì)算法。該算法將兩個原型濾波器的設(shè)計(jì)問題歸結(jié)為一個無約束優(yōu)化問題,將濾波器組的傳遞失真，混疊失真以及原型濾波器阻帶能量的加權(quán)和作為目標(biāo)函數(shù)。進(jìn)而，采用雙迭代機(jī)制來求解該優(yōu)化問題。在單步迭代中，運(yùn)用矩陣求逆的等效條件和Toeplitz矩陣求逆的快速算法，顯著地降低了迭代的計(jì)算代價(jià)。仿真對比表明,與已有的設(shè)計(jì)算法相比,新算法計(jì)算代價(jià)低 ,可以得到整體性能更好的濾波器組,并且可以快速設(shè)計(jì)大規(guī)模的濾波器組。
- 調(diào)制濾波器組 /
- 離散傅里葉變換 /
- 原型濾波器 /
- 無約束優(yōu)化 /
- 雙迭代算法
Abstract: This paper presents an efficient algorithm to design high-complexity Discrete Fourier Transform (DFT) modulated filter bank with double-prototype. The algorithm is based on unconstrained optimization, where the design problem is formulated into an unconstrained optimization problem, whose objective function is the weighted sum of the transfer distortion, the aliasing distortion of the filter bank, and the stopband energy of the Prototype Filters (PFs). The optimization problem can be efficiently solved by utilizing the bi-iterative scheme. The matrix inverse identity and the fast algorithm for Toeplitz matrix inversion are employed to dramatically reduce the computational cost of the iterative procedure. Numerical examples and compared tests to show that compared with the existing methods, the proposed method possesses much lower computational cost and can be used to design large-scale filter bank with better overall performance.
- Modulated filter bank /
- Discrete Fourier Transform (DFT) /
- Prototype Filters (PFs) /
- Unconstrained optimization /
- Bi-iterative scheme

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