利用四阶样条快速计算信号的希尔伯特变换

Fast Algorithm for the Hilbert Transform of a Signal by Using Cubic Splines

在有限区间内计算给定信号的希尔伯特变换是信号处理中的重要问题。三阶希尔伯特样条变换方法(Hilbert spline transform,HST)具有高阶计算精度和O(nlog n)计算速度的优点,但这种方法存在一个缺点,即B-样条节点必须不同于采样点,以避免计算中出现奇异值。为解决这一问题,本文采用四阶样条来进行希尔伯特样条变换;利用四阶样条对几个例子进行快速计算,说明给出方法的有效性。数值结果表明:本文所提方法在计算速度和精度方面都具有很好的性能。

The computation for the Hilbert transform of a given signal over a finite interval is an important problem in signal processing.Although the Hilbert spline transform(HST)method with order three demonstrates high order computational accuracy and the speed of O(nlog n),there is a disadvantage of this method:the grid of the B-spline knots must be different from the sample points to avoid singularities in the computation.To solve this problem,the spline function with order four is used to implement the Hilbert spline transform.To prove the effectiveness of the proposed method,several function of the Hilbert transform are calculated by using the cubic spline.Numerical results show that the proposed method has excellent performance in both computational speed and computational accuracy.