光纤陀螺随机误差的功率谱密度分别与频率的γ次方成反比,这类随机过程统称为1/fγ分形噪声,研究生成这类信号的方法对分析光纤陀螺的输出信号具有重要意义。分形噪声具有非平稳性、长程相关性、自相似性及1/fγ谱密度的特性,小波变换的多分辨分析是研究1/fγ噪声的良好工具。通过对高斯白噪声进行小波变换,再结合1/fγ噪声的方差特性,找到了满足1/fγ信号生成定理的各尺度正交小波系数,最后采用正交小波逆变换模拟出分形噪声,此方法可以产生任意噪声强度σ2、任意谱参数γ的1/fγ噪声。

The power spectrum density of random noise of Fiber Optic Gyroscope (FOG) is inversely proportional to frequencys power, and the random process was called 1/fγ fractal noise. The study on method for generating 1/fγ noise is very important for analyzing FOGs output signals. Fractal noise has the characteristics of nonstationarity, long-term correlation, self-similarity and 1/fγ spectral density with 1/fγ power law. The multi-resolution analysis of wavelet is a powerful tool for studying fractal noises. The wavelet is transformed by Gauss white noise firstly, then combing with the variance characteristics of 1/fγ noise, it is found that the orthonormal wavelet coefficient collection can satisfy the 1/fγ noise synthesis theory. The fractal noise is then simulated by using inverse orthonormal wavelet transform. The result proves that 1/fγ noise with any given amplitude and γ value within the limitation of wavelet regularity can be generated in this way.