基于分数阶傅里叶变换的探地雷达子波提取算法

针对探地雷达子波提取问题，提出了一种基于分数阶傅里叶变换的子波提取算法。假设探地雷达地下介质模型为线性系统并是时变的，并且子波在传播过程中不变，把子波和地层信息描述为一个时间的积分形式。分数阶傅里叶变换是酉变换，具有保范性，把子波的提取问题转化为在分数阶傅里叶变换域上的最优滤波问题。对分数阶傅里叶变换的阶数p在(－2,2]范围以1/300为步长进行了搜索，在分数阶傅里叶变换域上找到最优解，最后经过分数阶傅里叶变换反变换得到子波估计的时域信号。仿真实验首先验证了分数阶傅里叶变换最优滤波算法的正确性，然后利用探地雷达实验数据提取了子波，验证了该算法在提取子波中的有效性。

Wavelet Extraction of GPR Signals Based on Fractional Fourier Transform

Wavelet extraction algorithm based on fractional Fourier transform is presented in this paper.The wavelet and GPR medium is descried as a time integral based on the assumption that GPR medium model is linear time-varying systems and the wavelet is unchanging during propagation.Because fractional Fourier transform is a unitary transform and of norm-preserving,the wavelet extraction is transformed into optimal filtering problem in the fractional Fourier transform domain.The optimal solution is found by searching p in the range of(-2,2] to step 1/300.Finally,wavelet estimation signal in time-domain is obtained after an inverse fractional Fourier transform.The simulation shows that the optimal filtering algorithm of fractional Fourier transform is correct.The extracted wavelet from experiment GPR data shows that the wavelet extraction algorithm is valid.