补零离散傅立叶变换的插值算法

Interpolation Algorithm for Discrete Fourier Transform with Zero-Padding

插值离散傅立叶变换能提高正弦信号参数估计精度,但传统的比值插值算法只适用于数据长度等于离散傅立叶变换长度的场合。本文研究了补零离散傅立叶变换的插值问题,提出一种基于窗函数频谱一阶泰勒级数展开的插值算法,它与原比值法具有类似的形式和相同的计算量,是原比值法在数据长度小于或等于离散傅立叶变换长度时的扩展。性能分析和仿真试验还表明,补零离散傅立叶变换插值算法对频率偏差的敏感度降低,稳定性更好。

Interpolated discrete Fourier transform （DFT） improves the estimation accuracy of sinusoids. However,previous interpolation algorithms using the ratio of DFT coefficients assume that the data is as long as DFT length. In this paper we focus on the interpolation for DFT with zero-padding and propose a new algorithm based on the first order Taylor expansion of the window spectrum. It is similar to previous algorithms in formula and computing complexity, but is an extension applicable to DFT longer than the data. Both statistical analysis and simulation show that the interpolated DFT with zero-padding is less sensitive to the frequency drift and therefore has more stable performance than DFT without zero-padding.