Phase noise phenomenon explanation based multi-time variables differential equation technique

2016 ◽  
Author(s):  
Kunanon Kittipute ◽  
Panwit Tuwanut ◽  
Paramote Wardkein
Keyword(s):  
Differential Equation ◽  
Phase Noise ◽  
Time Variables ◽  
Noise Phenomenon

ASYMPTOTIC STOCHASTIC CHARACTERIZATION OF PHASE AND AMPLITUDE NOISE IN FREE-RUNNING OSCILLATORS

2011 ◽  
Vol 10 (02) ◽  
pp. 207-221 ◽  
Author(s):  
FABIO L. TRAVERSA ◽  
FABRIZIO BONANI
Keyword(s):  
Differential Equation ◽  
Phase Noise ◽  
Planck Equation ◽  
Integral Calculus ◽  
Amplitude Noise ◽  
Stochastic Characterization ◽  
Amplitude Fluctuations ◽  
Free Running ◽  
Definition Of

Starting from the definition of the stochastic differential equation for amplitude and phase fluctuations of an oscillator described by an ordinary differential equation, we study the associated Fokker–Planck equation by using tools from stochastic integral calculus, harmonic analysis and Floquet theory. We provide an asymptotic characterization of the relevant correlation functions, showing that within the assumption of a linear perturbative analysis for the amplitude fluctuations phase noise and orbital fluctuations at the same time are asymptotically statistically independent, and therefore the nonlinear perturbative analysis of phase noise recently derived still exactly holds even if orbital noise is taken into account.

Understanding Jitter and Phase Noise

2018 ◽  
Author(s):  
Nicola Da Dalt ◽  
Ali Sheikholeslami
Keyword(s):  
Phase Noise

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

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