基于DFT的信号子带分解与准确重构新方法

New Method for Subband Decomposition and Perfect Reconstruction Based on DFT

根据正交分解原理和离散傅里叶变换的物理意义,提出了一种分析滤波器组具有理想特性的信号分解与重构新方法(Discrete Fourier transform subband decomposition,DFTSD)。对于给定序列,通过离散傅里叶变换,将其变换到频域,通过谱线分组,在频域实现信号的分解,经反变换得到时域子带信号。频谱上无交叠的子带信号,从根本上解决了抽取过程所带来的带内混叠问题。综合滤波器组的设计仅需考虑内插后引入的镜像频率分量的滤除。实验结果表明,在无子带抽取和存在子带抽取情况下,重构信号与原信号的平均绝对误差在10-16量级。

How to process the non-ideal performance of analysis filter banks is a key problem. A novel method （discrete Fourier transform subband decomposition）（DFTSD） is proposed for the signal decomposition and reconstruction. For a given sequence, discrete Fourier transform （DFT） transforms it in to the frequency domain through grouping spectral line, the decomposition is to be implemented. The aliasing is eliminated by non-overlapping between adjacent subband spectrums. The only issue considered in design of synthesis filters is the filtering of image spectrum from interpolation. Experiments show that the absolute average error of the reconstruction signal to the primitive one is 10^-18at the level.