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The problem of estimating an unknown force driving a linear oscillator is revisited. When using linear measurement, feedback is often cited as a mechanism to enhance bandwidth or sensitivity. We show that as long as the oscillator dynamics…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
Long term behavior of nonlinear deterministic continuous time signals can be studied in terms of their reconstructed attractors. Reconstructed attractors of a continuous signal are meant to be topologically equivalent representations of the…
We consider the response of a memoryless nonlinear device that converts an input signal $\xi(t)$ into an output $\eta(t)$ that only depends on the value of the input at the same time, $t$. For input Gaussian noise with power spectrum…
When interference affecting various communication and sensor systems contains clearly identifiable outliers (e.g. an impulsive component), it can be efficiently mitigated in real time by intermittently nonlinear filters developed in our…
We analyze a global sensing scenario in which the frequency of a monitored Kerr parametric oscillator is estimated assuming limited prior information. The frequency is estimated in real-time by continuously monitoring the oscillator…
Nonlinear activation functions are widely recognized for enhancing the expressivity of neural networks, which is the primary reason for their widespread implementation. In this work, we focus on ReLU activation and reveal a novel and…
Rectified linear unit (ReLU) is a widely used activation function for deep convolutional neural networks. However, because of the zero-hard rectification, ReLU networks miss the benefits from negative values. In this paper, we propose a…
For many machine learning applications, a common input representation is a spectrogram. The underlying representation for a spectrogram is a short time Fourier transform (STFT) which gives complex values. The spectrogram uses the magnitude…
Time-frequency (TF) representations of time series are intrinsically subject to the boundary effects. As a result, the structures of signals that are highlighted by the representations are garbled when approaching the boundaries of the TF…
The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum. Practitioners seeking low-dimensional summary measures…
Vibrational resonance focuses on the resonance behavior of a nonlinear system when it is subjected to both a weak low-frequency characteristic signal and a high-frequency auxiliary signal. A traditional Duffing system has a fixed natural…
In this paper, we propose novel quaternion activation functions where we modify either the quaternion magnitude or the phase, as an alternative to the commonly used split activation functions. We define criteria that are relevant for…
The Fast Fourier Transform (FFT) is a fundamental tool for signal analysis, widely used across various fields. However, traditional FFT methods encounter challenges in adjusting the frequency bin interval, which may impede accurate spectral…
Accounting for phase variability is a critical challenge in functional data analysis. To separate it from amplitude variation, functional data are registered, i.e., their observed domains are deformed elastically so that the resulting…
We investigate the dynamics of mechanical resonators subject to excitations comprising of an oscillating or harmonic part, whose amplitude decays exponentially in time. We call these complex frequency excitations and show that the resulting…
Feedback amplification is a key technique for synthesizing various important functionalities, especially in electronic circuits involving op-amps. This paper presents a quantum version of this methodology, where the general phase-preserving…
Location of non-stationary forced oscillation (FO) sources can be a challenging task, especially in cases under resonance condition with natural system modes, where the magnitudes of the oscillations could be greater in places far from the…
Activation function is a key component in deep learning that performs non-linear mappings between the inputs and outputs. Rectified Linear Unit (ReLU) has been the most popular activation function across the deep learning community.…
A system obeying the harmonic oscillator equation of motion can be used as a force or proper acceleration sensor. In this short review we derive analytical expressions for the sensitivity of such sensors in a range of different situations,…