一种基于Mellin变换的水声宽带相关模糊函数的快速算法

提出了一种基于Mellin 变换的快速算法,其特点是在给定的某一时刻得到不同尺度下的变换结果,算法的运算量与待分析的时延成正比,而在固定时刻下的运算量为两个2M点的FFT和一次2M点复数乘法(M为待分析的尺度的个数).该算法的优点是实时性好,且适合于水声信号领域尺度跨度小、尺度分析较细的特点,并给出了与直接法、CZT法的比较结果.

A fast algorithm of wide-band correlative ambiguity function based on Mellin transform

In this paper, a fast algorithm to calculate WBCAF based on Mellin transform is provided, and it has the characteristics that it calculates the coefficients of different scales simultaneously at a certain time instant. The computational complexity is proportional to the length of data being processed, and includes two FFTs and a complex multiplication all of length 2M at each time point(M is the number of scales). It is shown that this fast algorithm is suitable to signal analysis at scales over a relatively narrow span and with fine interval, especially in water signal processing field. The comparative result with direct method and CZT algorithm is also presented.