近似完全重构交替离散傅里叶变换调制滤波器组

Near Perfect Reconstruction Interleaved Discrete Fourier Transform Modulated Filter Bank

针对离散傅里叶变换调制滤波器组(DFTMFB)阻带衰减小的问题,提出了一种交替离散傅里叶变换调制滤波器组(IDFTMFB)的设计方法.其分析滤波器由2个分析原型滤波器经复指数交替调制得到,综合滤波器由2个原型滤波器按同一调制方式得到.所采用的交替调制方式使IDFT-MFB在结构的设计上具有更多的灵活性.按照滤波器组的通带、阻带和系统失真的要求,IDFT-MFB原型滤波器的设计被转化为一个非线性优化问题,避免了传统的DFTMFB中连续参数的离散化运算,算法更为简单.仿真结果表明,与传统的DFTMFB设计方法相比,IDFTMFB的设计方法使得复调制滤波器组的阻带衰减提高了约3 dB,输出失真减小了约12 dB,而且输出混叠减小了约1 dB.

Aiming at the problem of small stopband attenuation of discrete Fourier transform modulated filter bank （DFTMFB）, a method that is used to design novel interleaved discrete Fourier transform modulated filter banks （IDFTMFB） is presented. The analysis filter bank of IDFTMFB is generated by alternately modulating two analysis prototype filters with complex exponential function, and the synthesis filter bank of IDFTMFB is generated from two synthesis prototype filters via the same modulating manner. The interleaved modulation method used by IDFTMFB provides more flexibility in its structure design. Based on the requirements on the passband, stopband, and system distortion of the filter bank, the design of the IDFTMFB prototype filters is converted into a non-linear optimization problem. Since the discretization operation of continuous parameter in the design of conventional DFTMFB is avoided, the proposed algorithm is simple. Simulation results show that the improvement on the stopband attenuation of the complex modulated filter bank obtained by the proposed method is approximately 3 dB higher than the traditional DFTMFB method, the improvement on the output distortion is up to approximately 12 dB, while the output aliasinu is reduced approximately 1 dB.