EFFICIENT INCREMENTAL SIMULATION OF “1/f” NOISES

Abstract

Large-scale simulations and analysis of the original powers of 2 geometric source sum algorithm for simulating [Formula: see text] noise confirm that it provides a reasonably accurate approximation to an exact [Formula: see text] spectral density with a Gaussian amplitude distribution over any arbitrarily large frequency range. This incremental algorithm is computationally efficient with a computation time, after initialization, that varies linearly with the number of samples generated. A new variation allows non-integer and random ratios for the geometric sequence that reduces variations about the exact power-law spectral density and, by varying individual source amplitudes, produces generalized [Formula: see text] noises.