TY - JOUR
T1 - Discrete Simulation of Colored Noise and Stochastic Processes and 1/fα Power Law Noise Generation
AU - Kasdin, N. Jeremy
N1 - Funding Information:
Manuscript received August 9, 1993; revised January 30, 1995. This work was supported by NASA Contract NAS8-36125. The author is with the W.W .H ansen Experimental Physics Laboratory, Relativity MissiodGravity Probe B, Stanford University, Stanford, CA 94305-4085 USA. IEEE Log Number 9410317.
PY - 1995/5
Y1 - 1995/5
N2 - This paper discusses techniques for generating digital sequences of noise which simulate processes with certain known properties or describing equations. Part I of the paper presents a review of stochastic processes and spectral estimation (with some new results) and a tutorial on simulating continuous noise processes with a known autospectral density or autocorrelation function. In defining these techniques for computer generating sequences, it also defines the necessary accuracy criteria. These methods are compared to some of the common techniques for noise generation and the problems, or advantages, of each are discussed. Finally, Part I presents results on simulating stochastic differential equations. A Runge–Kutta (RK) method is presented for numerically solving these equations. Part II of the paper discusses power law, or 1/fα, noises. Such noise processes occur frequently in nature and, in many cases, with nonintegral values for α. A review of 1/f noises in devices and systems is followed by a discussion of the most common continuous 1/f noise models. The paper then presents a new digital model for power law noises. This model allows for very accurate and efficient computer generation of 1/fα noises for any a. Many of the statistical properties of this model are discussed and compared to the previous continuous models. Lastly, a number of approximate techniques for generating power law noises are presented for rapid or real time simulation.
AB - This paper discusses techniques for generating digital sequences of noise which simulate processes with certain known properties or describing equations. Part I of the paper presents a review of stochastic processes and spectral estimation (with some new results) and a tutorial on simulating continuous noise processes with a known autospectral density or autocorrelation function. In defining these techniques for computer generating sequences, it also defines the necessary accuracy criteria. These methods are compared to some of the common techniques for noise generation and the problems, or advantages, of each are discussed. Finally, Part I presents results on simulating stochastic differential equations. A Runge–Kutta (RK) method is presented for numerically solving these equations. Part II of the paper discusses power law, or 1/fα, noises. Such noise processes occur frequently in nature and, in many cases, with nonintegral values for α. A review of 1/f noises in devices and systems is followed by a discussion of the most common continuous 1/f noise models. The paper then presents a new digital model for power law noises. This model allows for very accurate and efficient computer generation of 1/fα noises for any a. Many of the statistical properties of this model are discussed and compared to the previous continuous models. Lastly, a number of approximate techniques for generating power law noises are presented for rapid or real time simulation.
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U2 - 10.1109/5.381848
DO - 10.1109/5.381848
M3 - Article
AN - SCOPUS:0029304629
SN - 0018-9219
VL - 83
SP - 802
EP - 827
JO - Proceedings of the Institute of Radio Engineers
JF - Proceedings of the Institute of Radio Engineers
IS - 5
ER -