小波包变换及正弦函数模拟消除50 Hz工业干扰

陷波技术是用于消除50Hz工业干扰的一种有效工具,由于其采用频率切除技术,故在消除50Hz工业干扰的同时,使50Hz及其附近的有效信号受到损失,给后续处理带来不利影响。为此,提出采用正弦函数来模拟50Hz工业干扰,并采用减法运算从数据中减去它,达到消除50Hz工业干扰又使有效波损失减小到最小的目的。为了使去噪处理仅在有限频带上进行,采用小波包变换分解来得到50Hz工业干扰所在频带;为使在有限频带内模拟50Hz工业干扰实现方便,采用了卷积型小波包变换来得到含有50Hz工业干扰且其小波系数保持了与原始记录相同的样点数。最后给出了理论模型测试结果,并应用实际单炮记录进行了对比处理。

基于维纳滤波的50Hz工业干扰去噪方法研究及应用

50Hz工业干扰是地震资料中一种常见的噪声，由于它与有效信号的频率范围重叠，影响了地震资料的品质。常规的消除50Hz噪声方法是陷波处理，它在切除噪声的同时，也切除了有效信号。本文研究了一种基于最小平方滤波原理的消除50Hz干扰波算法。它通过设计一个参考正弦道，并通过维纳滤波器来调整该参考道的振幅和相位．从而使其与数据道中的50Hz噪声达到最佳匹配。在时域，用数据道减去参考道，即可达到单频去噪的目的。由于该方法不是在频率域实现，既可准确实现单频去噪，又可避免吉布斯现象的发生，因此有较高的保真度。

A generalized sinusoidal model and its applications

A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation of the generalized model was given. Simulations were conducted with different power values. The results show that the solution of the generalized equation is a periodic function. The expressions of the amplitude and the period(frequency) of the generalized equation were derived by the physical method. All the simulation results coincide with the calculation results of the derived expressions. A special function also was deduced and proven to be convergent in the theoretical analysis. The limit value of the special function also was derived. The generalized model can be used in solving a type of differential equation and to generate periodic waveforms.