一对平衡双正交尺度函数的构造

给出了一种构造平衡尺度向量的新方法,旨在解决非平衡双正交多小波在应用中遇到的实际困难。基于给定的一对具有紧支撑的双正交尺度函数,构造性的生成一对新的尺度函数,使之仍保持双正交性;进一步地,当原尺度函数具有一定逼近阶时,对滤波器加以若干条件设计非线性方程组,还可使新的尺度函数具有相应的平衡阶。     

A new method for detecting line spectrum of ship-radiated noise using Duffing oscillator

A detection scheme for line spectrum of ship-radiated noise is proposed using Duffing oscillator. The chaotic trajectory of Duffing oscillator is analyzed and the state equation of the system is improved to detect weak periodic signals in different frequencies. According to the simulation results, the phase transforms of Duffing oscillator are sensitive to periodic signals and immune to the random noise and the periodic interference signals which have larger angular frequency difference from the referential signal. By employing Lyapunov exponents in the field of detection as the criteria for chaos, the phase transforms of dynamic behaviors in quantity are successfully determined. Meanwhile, the threshold value in critical state has been evaluated more accurately. Based on the phase transforms of Duffing oscillator, a new method for detecting line spectrum of ship-radiated noise is given. Three types of ship-radiated noise signals are analyzed and the values of line spectrum are acquired successfully by this method. The experimental results show that this method has high sensitivity and high resolution.