THE ALGORITHM OF FORMATION OF CARRIER OSCILLATIONS FOR A LINEAR COMMUNICATION CHANNEL WITH ADDITIVE GAUSSIAN WHITE NOISE

2010 ◽  
Vol 69 (11) ◽  
pp. 993-1004
Author(s):  
K. A. Batenkov
Keyword(s):  
White Noise ◽  
Communication Channel ◽  
Gaussian White Noise ◽  
Additive Gaussian White Noise

Testing for the presence of sinusoidal components

1986 ◽  
Vol 23 (A) ◽  
pp. 201-210 ◽  
Author(s):  
B. G. Quinn
Keyword(s):  
Time Series ◽  
White Noise ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Gaussian White Noise ◽  
Ratio Test ◽  
Additive Gaussian White Noise

Approximate and asymptotic distributional results are obtained for the likelihood ratio test of the hypothesis that a time series is composed from s sinusoidal components, at unknown frequencies, with additive Gaussian white noise, against the hypothesis that there are an additional r sinusoidal components at unknown frequencies. The work extends that of Fisher (1929), and contains a number of simulations illustrating the results.

Probabilistic Solution of Vibro-Impact Systems Under Additive Gaussian White Noise

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
H. T. Zhu
Keyword(s):  
White Noise ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Solution Procedure ◽  
Additive Gaussian White Noise ◽  
Stationary Probability Density Function ◽  
Probabilistic Solution ◽  
Zero Offset ◽  
Polynomial Closure

This paper presents a solution procedure for the stationary probability density function (PDF) of the response of vibro-impact systems under additive Gaussian white noise. The constraint is a unilateral zero-offset barrier. The vibro-impact system is first converted into a system without barriers using the Zhuravlev nonsmooth coordinate transformation. The stationary PDF of the converted system is governed by the Fokker–Planck equation which is solved by the exponential-polynomial closure (EPC) method. A vibro-impact Duffing oscillator with either elastic or lightly inelastic impacts is considered in a numerical analysis. Meanwhile, the level of nonlinearity in displacement is also examined in this study as well as the case of negative linear stiffness. Comparison with the simulated results shows that the EPC method can present a satisfactory PDF for displacement and velocity when the polynomial order is taken as 4 in the investigated cases. The tail of the PDF also works well with the simulated result.

Testing for the presence of sinusoidal components

1986 ◽  
Vol 23 (A) ◽  
pp. 201-210 ◽  
Author(s):  
B. G. Quinn
Keyword(s):  
Time Series ◽  
White Noise ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Gaussian White Noise ◽  
Ratio Test ◽  
Additive Gaussian White Noise

Approximate and asymptotic distributional results are obtained for the likelihood ratio test of the hypothesis that a time series is composed from s sinusoidal components, at unknown frequencies, with additive Gaussian white noise, against the hypothesis that there are an additional r sinusoidal components at unknown frequencies. The work extends that of Fisher (1929), and contains a number of simulations illustrating the results.

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