A procedure for efficient generation of 1/fβ noise sequences

This paper presents a simple, efficient and fast procedure for generation of 1/f(beta) noise sequences. The proposed procedure is based on the impulse invariance method applied to the impulse response of the ideal fractional order integrator whose order alpha = beta/2 is between 0 and 1. First, an optimal value for the initial value of the impulse response is obtained by minimizing a least squares error criterion and then any of the well-established signal modeling techniques can be employed for the parameterization of the discrete impulse response by pole-zero models. For a given model order, the approximation accuracy depends on the signal modeling technique used. An illustrative example is presented to demonstrate the effectiveness of the method.