周期非均匀采样信号的重建中的优化子频带划分

Optimal Subband Partition for Reconstruction of Bandlimited Signals from Periodically Nonuniform Samples

对于周期非均匀采样,由于每个均匀采样流的采样率通常都是小于Nyquist率的,因此,采样信号频谱中会发生频率混叠。这表明在采样信号的重建频带内将会有多于1的谱分量。因为不是所有的与重建频带相交的谱分量都会覆盖整个重建频带,所以有必要将重建频带分成若干个子频带进行分析,构造内插函数,这样有利于减小重建所必需的最小采样率。本文提出一种优化的子频带划分方法,通过该方法在重建频带上定义子频带,能在保证重建所需的采样率最低的情况下使子频带的个数最少,这对于简化内插滤波器的结构有重要的意义。

In periodically nonuniform sampling, the sampling rate for a single sampling channel is usually less than the Nyquist rate and accordingly the spectrum of each sample stream is aliasing. This indicates that there will be more than one spectral replica in the reconstructed band of a sampled signal. The reconstruction strategy from periodically nonuniform samples is set up with respect to spectral replica positions and numbers within the reconstructed band. For not all the spectral replicas will cover the whole reconstructed band, it is natural and necessary to partition the reconstructed band into subbands to analyze and derive sampling and reconstruction specifications ： such as filter shapes, sampling orders （channels）. The paper proposes an optimal partition of subbands in reconstruction from periodically nonuniform samples by making the numbers of spectral replicas in subbands equal. The partition scheme ensures the minimum sampling orders under a given sampling rate for a single channel as well as the minimum number of subbands, which in turn suggests a simpler filter shape.