Gleeson James P
Applied Mathematics, University College Cork, Ireland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 1):011106. doi: 10.1103/PhysRevE.72.011106. Epub 2005 Jul 18.
An exactly solvable model generating a continuous random process with a 1/f power spectrum is presented. Examples of such processes include the angular (phase) speed of trajectories near stable equilibrium points in two-dimensional dynamical systems perturbed by colored Gaussian noise. An exact formula giving the correlation function of the 1/f noise in terms of the correlation of the perturbing colored noises is derived, and used to show that the 1/f spectrum is found in a wide variety of cases. The 1/f noise is non-Gaussian, as demonstrated by calculating its one-time probability distribution function. Numerical simulations confirm and extend the theoretical results.
提出了一个能生成具有1/f功率谱的连续随机过程的精确可解模型。此类过程的例子包括受有色高斯噪声扰动的二维动力系统中稳定平衡点附近轨迹的角（相位）速度。推导了一个根据扰动有色噪声的相关性给出1/f噪声相关函数的精确公式，并用于表明在多种情况下都能发现1/f谱。通过计算其一时间概率分布函数证明，1/f噪声是非高斯的。数值模拟证实并扩展了理论结果。
