生成粉红噪声的ARMA模型

ARMA Model for Generating Pink Noise

针对现有粉红噪声的生成方法所存在的计算过程复杂,与理想粉红噪声相比偏差较大等问题,本文提出了一种利用自回归滑动平均(Auto-regressive moving average,ARMA)模型法生成粉红噪声的新方法。首先,构造一个待定系数的ARMA模型,并通过Z变换和功率谱估计的公式进行推导;其次,利用已知的粉红噪声模拟滤波器的传递函数H(s)和双线性Z变换法推导出IIR数字滤波器的传递函数H(z),进而得到粉红噪声的ARMA模型;最后,利用MATLAB对生成的粉红噪声进行功率谱估计并与理想的粉红噪声进行对比。由MATLAB仿真结果可知,利用该方法生成的粉红噪声与理想的粉红噪声拟合度更高,完全符合粉红噪声的各项性能要求。

Aiming at such problems as the complex calculating process, the large deviation compared with ideal pink noise on the existing generation methods of pink noise, a new generating method of pink noise using auto-regressive moving average （ARMA） model is proposed. Firstly, an ARMA model of undetermined coefficients is constructed, and the formula is de- rived by Z transform and power spectrum estimation. Secondly the known pink noise analog filter transfer function H（s） and the principle of bilinear Z transformation method are utilized to derive IIR digital filter transfer function H（z）, and then the ARMA model of pink noise can be obtained. Finally, its power spectrum estimation is performed using MATLAB and results are compared with the ideal pink noise. As the simulation results shown, the method has a higher fitting degree with ideal pink noise and complies with the performance requirements of pink noise.