A method of rapidly generating 1/f^γ fractal signal

Fractal noise is the main stochastic noise of Fiber Optic Gyroscope (FOG). For the common spectral exponent γ, a Fractional Differencing (FD) method is put forward for rapidly generating fractal signal in simulation. First, its fractional differential expression based on Fractional Brownian Motion (FBM) model is derived. Then the derived expression is transformed into a discrete domain by substituting FD operator, thus fractal signal can be expressed as the FD form of Gaussian White Noise (GWN). Once a spectral exponent γ is specified, the FD matrix can be constructed, and by convoluting with GWN series, the obtained result is the desired fractal series. In the end, by comparing the simulation performances with those of the fractal series generated by the integration method of Fast Fourier Transform (FFT) and wavelet transform respectively, the feasibility and the superiority of the proposed method is demonstrated. The FD mainly involves convolution operation, therefore its computation is simple, and can meet the requirement for rapidly generating fractal signal in simulation.