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Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture.…
Existing algorithms for fitting the parameters of a sinusoid to noisy discrete time observations are not always successful due to initial value sensitivity and other issues. This paper demonstrates the techniques of FIR filtering, Fast…
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of…
Fluctuation-enhanced sensing comprises the analysis of the stochastic component of the sensor signal and the utilization of the microscopic dynamics of the interaction between the agent and the sensor. We study the relationship between the…
Time, and equivalently frequency, is the most precisely measured physical quantity. It is therefore inevitable that virtually all domains of engineering and physics need reference oscillators. The oscillator noise can be decomposed into…
We describe the measurement and modeling of amplitude noise and phase noise in ultra-high Q nanomechanical resonators made from stoichiometric silicon nitride. With quality factors exceeding 2 million, the resonators' noise performance is…
Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in…
We develop an error mitigation method for the control-free phase estimation. We prove a theorem that under the first-order correction, the noise channels with only Hermitian Kraus operators do not change the phases of a unitary operator,…
We exercise rapid and fine control over the phase of light by transferring digitally gen- erated phase jumps from radio frequency (rf) electrical signals onto light by means of acousto-optic interaction. By tailoring the statistics of phase…
A common problem to signal processing are biases introduced by correlated noise. When quantifying time delays between two signals, mixed noise introduces a bias towards zero delay in conventional delay estimates based on the cross- or…
Fuzzy Transform (F-transform) has been introduced as an approximation method which encompasses both classical transforms and approximation methods studied in fuzzy modeling and fuzzy control. It has been proved that, under some conditions,…
We study a diagnosis scheme to reliably detect the active mode of discrete-time, switched affine systems in the presence of measurement noise and asynchronous switching. The proposed scheme consists of two parts: (i) the construction of a…
Changes in parameters of a physical device can eventually lead to catastrophic failure. This paper discusses a parameter estimation method based on synchronization between a model and time series data. In particular, we examine the…
The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the…
The spectral coherence properties of supercontinuum generation in polarization-maintaining all-normal dispersion fibers are investigated. Stochastic phase noise induced by energy fluctuations, along with spectrally-resolved…
A general approach to consider spatially extended stochastic systems with correlations between additive and multiplicative noises subject to nonlinear damping is developed. Within modified cumulant expansion method, we derive an effective…
Quantum mechanics imposes that any amplifier that works independently on the phase of the input signal has to introduce some excess noise. The impossibility of such a noiseless amplifier is rooted into unitarity and linearity of quantum…
We present a comparative study of the influence of dispersion induced phase noise for CO-OFDM systems using Tx channel multiplexing and Rx matched filter (analogue hardware based); and FFT multiplexing/IFFT demultiplexing techniques…
We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in Optical Parametric Oscillators. This additional phase noise reduces…
Phase estimation is the most investigated protocol in quantum metrology, but its performance is affected by the presence of noise, also in the form of imperfect state preparation. Here we discuss how to address this scenario by using a…