插值重建的分数阶傅里叶域分析

The Analysis of Reconstruction by Interpolation in the Fractional Fourier Domain

建立在傅里叶变换基础上的传统插值重建理论已不适用于基于分数阶傅里叶变换的SAR算法,文中对插值重建理论在分数阶傅里叶域作了进一步的分析和仿真。首先依据分数阶卷积的概念从分数阶傅里叶域的角度分析了采样信号的重建方程。其次从工程应用出发,进行了有限数目卷积核的插值重建误差分析。最后,给出了卷积核的截断归一化公式。可以发现利用分数阶卷积的插值核数目大于16即可,且需要保证移动后的样本位置不远离原卷积核的样本位置。

The conventional reconstruction theory by interpolation is based on the Fourier transform, has not fit for the SAR algorithms based on the fractional Fourier transform. In this paper, reconstruction by interpolation is analyzed and simulated in the fractional Fourier domain further. Firstly, the reconstruction formula of a sampled signal was analyzed in the fractional Fourier domain according to the fractional convolution. Secondly, as for engineering application, the error analysis of reconstruction by interpolation was made in according to finite convolution functions. Finally, the normalization formulas of intercepted convolution functions were shown. It＇s conchided that the proper number of samples for the fractional convolution is about 16, and the shift location should be near to the positions of those samples.