Related papers: Optical Costas loop: pull-in range estimation and …
This survey is devoted to the dynamic analysis of the Costas loop. In particular the acquisition process is analyzed in great detail. Acquision is most conventiently described by a number of frequency and time parameters such as lock-in…
The Costas loop is a modification of the phase-locked loop circuit, which demodulates data and recovers carrier from the input signal. The Costas loop is essentially a nonlinear control system and its nonlinear analysis is a challenging…
Nonlinear analysis of the phase-locked loop (PLL) based circuits is a challenging task, thus in modern engineering literature simplified mathematical models and simulation are widely used for their study. In this work the limitations of…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
Rigorous nonlinear analysis of the physical model of Costas loop --- a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation…
Nonlinear analysis of the classical phase-locked loop (PLL) is a challenging task. In classical engineering literature simplified mathematical models and simulation are widely used for its study. In this work the limitations of classical…
Phase-locked loops (PLL), Costas loops and other synchronizing circuits are featured by the presence of a nonlinear phase detector, described by a periodic nonlinearity. In general, nonlinearities can cause complex behavior of the system…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
We address the problem of motion estimation in images operating in the frequency domain. A method is presented which extends phase correlation to handle multiple motions present in an area. Our scheme is based on a novel Bilateral-Phase…
In the present work the model of PLL with impulse signals and active PI filter in the signal's phase space is described. For the considered PLL the lock-in range is computed analytically and obtained result are compared with numerical…
We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilised to produce squeezed states, is applied to a general…
Optomechanical oscillators (OMOs) combine the co-existing high quality factor mechanical and optical resonances in an integrated device to realize low phase noise RF oscillations. While several attempts have been demonstrated towards…
Optomechanical systems are known to exhibit a rich set of complex dynamical features including various types of chaotic behavior and multi-stability. Although this exotic behavior has attracted an intense research interest, the utilization…
We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular…
Stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
Stability assessment methods for dynamical systems have recently been complemented by basin stability and derived measures, i.e. probabilistic statements whether systems remain in a basin of attraction given a distribution of perturbations.…
The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…
We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the state space, having a constant mean first return time. The…
We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [Tsang, Shapiro, and Lloyd, Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to…