基于零阶贝塞尔函数加权的三角窗切趾函数

Improved Triangular Window Apodization Function Based on Zero-Order Bessel Function

傅里叶变换是干涉图分析处理的常用方法,由于截断效应,对样本数据直接进行傅里叶变换时会发生频谱泄漏,常采用加切趾函数的方法减小泄漏。首先分析多种常见切趾函数的性能,研究切趾函数主瓣宽度与旁瓣衰减对频谱泄漏的影响;在此基础上,提出一种基于零阶贝塞尔函数加权的三角窗切趾函数,对三角窗函数加权,使其旁瓣衰减加快。实验结果表明:采用提出的改进的三角窗切趾函数能有效抑制频谱泄漏;相比于三角窗,改进的三角窗切趾函数平均峰-峰值信噪比提升了4.9%,方均根值信噪比提升了3.5%,优于常见窗中最优的布莱克曼窗。改进的三角窗切趾函数的主瓣宽度为0.043π,与汉宁窗接近,具有较高的频率分辨率。

The Fourier transform is commonly used in interferogram analysis.However,owing to the truncation effect,the direct application of Fourier transform for sampled data tends to cause spectral leakage.To address this problem,the apodization function is often adopted.In this paper,we first analyze the performances of different interferogram apodization functions.Then,the effects of the mainlobe width and sidelobe attenuation of the apodization functions on spectral leakage are studied.Finally,we propose an improved triangular window apodization function based on the zero-order Bessel function.It can accelerate the sidelobe attenuation by weighing the triangular window function.Results from extensive experiments show that the improved triangular window apodization function can effectively suppress energy leakage.When compared to the triangular window,this study suggests that the proposed method improves the mean of the peak-to-peak signal-to-noise ratio by 4.9%and the root mean square signal-to-noise ratio by 3.5%.In addition,these results are more accurate than that achieved using the Blackman window.Further,the mainlobe width of the improved triangular window apodization function is 0.043π,which is closed to that of the Hanning window.Therefore,our proposed method proffers a good frequency resolution.