基于小波降噪的稀疏傅里叶变换时延估计

Time Delay Estimation for Sparse Fourier Transform Based on Wavelet Denoising

稀疏傅里叶变换时延估计具有较低的运算时间复杂度,但在低信噪比时无法准确估计出时延。针对稀疏傅里叶变换时延估计在噪声干扰下时延估计精度下降的缺点,提出了基于小波降噪的稀疏傅里叶变换时延估计算法。算法利用小波降噪方法处理接收到的信号,再对降噪后的信号进行稀疏傅里叶变换广义相关,通过检测相关函数的谱峰得到估算的时延值。实验仿真以及对实测数据的验证均表明,在低信噪比条件下,基于小波降噪的稀疏傅里叶变换时延估计算法在保证数据高处理速度的同时,具有较好的抗噪性以及较高的时延估值精确度。

Sparse Fourier transform delay estimation has a lower computational time complexity, but it can not accurately estimate the delay at low signal to noise ratio（SNR）. In order to overcome the shortcomings of time delay estimation of sparse Fourier transform under noise interference, a new algorithm for time delay estimation of sparse Fourier transform based on wavelet denoising is proposed. The wavelet denoising method was used to process the received signal, and then the denoised signal was subjected to the sparse Fourier transform generalized correlation, and the estimated delay value was obtained by detecting the spectral peak of the correlation function. The experimental simulations and the verification of measured data all show that the improved algorithm has good noise immunity and high accuracy of time delay estimation while ensuring high data processing speed under low SNR condition.