AR 与 ARMA 有色噪声的生成方法

Efficient Generation of Colored Noise with AR and ARMA Data Model and Its Software Implementation

基于自回归（ＡＲ）与自回归滑动平均（ＡＲＭＡ）模型，讨论了两种有色噪声的软件生成方法，可使输出序列无起始瞬变现象。给定功率谱函数结构时采用递推算法；给定滤波器系数时采用步降法。分别给出了滤波器的两种设计流程。通过设置滤波器的初始状态，使得在白噪声激励下滤波器的输出序列稳定，无起始瞬变现象。该方法在实际工作中得到应用，软件仿真表明两种设计方法都能满足仿真的设计要求。

With autoregression and the autoregressive moving average data model,two new methods are discussed for efficiently generating colored noise without transient. The first one, the “Recursive Method”, is used when the data of the desired power spectral density are given; and the second one, the “Step down Method”, is used when the coefficients of the filter are known. Under the condition of the minimum mean square,two flow diagrams of the filter design are presented respectively. Instead of discarding initial samples to account for the transient,the approach proposed here is to set the initial conditions of the filter so that the output process is stationary. The methods discussed above have been tested under real work conditions and the software simulations have confirmed the design requirements.