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This paper presents a new procedure for generating 1/fbeta noise sequences by filtering Gaussian white noise through a recursive filter approximating a discrete-time fractional order integrator. Power series expansion and deterministic signal modeling techniques were combined to determine a rational transfer function to approximate the ideal discrete fractional transfer function resulting from Al-Alaoui's rule raised to the power of the fractional order of integration. The proposed approach is computationally more efficient and more accurate than infinite impulse response truncation. Numerical results are provided to demonstrate the performance of the proposed method.