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The output **frequency** response of a nonlinear system.
... The restoring force of a bilinear **oscillator**.
... The output **frequency** response of a linear system.
... Bilinear **oscillator**... The polynomial approximation result for a bilinear **oscillator**
... Nonlinear output **frequency** response function... Bilinear **oscillator** model.
... In this paper, the new concept of nonlinear output **frequency** response functions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the generalized **frequency** response functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs. Then, beginning with the demonstration that a bilinear **oscillator** can be approximated using a polynomial-type nonlinear **oscillator**, the NOFRFs are used to analyse the energy transfer phenomenon of bilinear **oscillators** in the **frequency** domain. The analysis provides insight into how new **frequency** generation can occur using bilinear **oscillators** and how the sub-resonances occur for the bilinear **oscillators**, and reveals that it is the resonant **frequencies** of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear **oscillator** model.

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Dominant **frequency**... The first and the second dominant **frequencies** variation with the steam mass flux.
... The first and the second dominant **frequencies** variation with the water temperature.
... The dominant **frequency** regime map.
... Pressure **oscillation**... **Frequency** spectrums of pressure **oscillation** at different water temperatures and steam mass flux.
... Experimental investigations and analysis on the dominant **frequency** of pressure **oscillation** for sonic steam jet in subcooled water have been performed. It was found that sometimes there is only one dominant **frequency** for pressure **oscillation**, and sometimes there is a second dominant **frequency** for pressure **oscillation**. The first dominant **frequency** had been investigated by many scholars before, but the present study mainly investigated the characteristics of the second dominant **frequency**. The first dominant **frequency** is mainly caused by the periodical variation of the steam plume and the second dominant **frequency** is mainly caused by the generating and rupture of the large steam bubbles. A dominant **frequency** regime map related to the water temperature and steam mass flux is given. When the water temperature and the steam mass flux are low, there is only one dominant **frequency** of pressure **oscillation**. When the water temperature or the steam mass flux is high, the second dominant **frequency** appears for pressure **oscillation**. The second dominant **frequency** decreases with the increasing water temperature and steam mass flux. Meanwhile, the second dominant **frequency** at high steam mass flux and water temperature is lower than the first dominant **frequency** at low steam mass flux and water temperature. A dimensionless correlation is proposed to predict the second dominant **frequency** for sonic steam jet. The predictions agree well with the present experimental data, the discrepancies are within ±20%.... The dominant **frequencies** in different measurement points by Qiu et al. [14].

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Low-**frequency** **oscillations**... Undamped swing curve: one **oscillation** mode.
... Un-damped swing curve with two **oscillation** modes: f1=0.4, f2=0.5Hz and σ1=−0.025, σ2=+0.037s−1.
... Low-**frequency** **oscillations** in the interconnected power systems are observed all around the electrical grids. This paper presents a novel technique for analyzing the low-**frequency** **oscillations** in power system networks. The proposed technique is a dynamic estimator based on stochastic estimation theory which is suitable for estimating parameters on-line. The method uses digital set of measurements for power system swings to perform the analysis process digitally. The goal is to estimate the amount of damping in the swing curve as well as the **oscillation** **frequency**. The problem is formulated and presented as a stochastic dynamic estimation problem. The proposed technique is used to perform the estimation process. The algorithm tested using different study cases including practical data. Results are evaluated and compared to those obtained using other conventional methods to show the capabilities of the proposed method.

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Diagram of the MNI detector. (A) baseline detector. (B) HFOs detection in channels with baseline. (C) HFOs detection in channels with continuous high **frequency** activity. If more than 5s/min of baselines are found, HFOs are detected with respect to the baseline segments (B). If less than 5s/min of baseline were detected, HFOs are detected with respect to the entire EEG segment in an iterative way (C). WE: wavelet entropy; Rxx: autocorrelation; th: Threshold.
... High **frequency** **oscillations**... Histogram of peak **frequencies** of FRs not occurring with ripples. Out of the 7994 PosAnd HFOs, 554 corresponded to FR that did not co-occur with a visually marked ripple. The peak **frequencies** of these events included not only the 250–500Hz band but also the 80–250Hz band. All these events were visually marked as FR using a high-pass filter at 250Hz. Two examples are presented. Top: FR with a peak **frequency** at 150Hz; Bottom: FR with a peak at 265Hz. The unfiltered EEG, the filtered EEG above 80Hz and the filtered EEG above 250Hz are shown. The **oscillations** become visible only when filtering above 250Hz.
... High **frequency** **oscillations** (HFOs) are a biomarker of epileptogenicity. Visual marking of HFOs is highly time-consuming and inevitably subjective, making automatic detection necessary. We compare four existing detectors on the same dataset.

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Cortical distributions of SEPs and high-**frequency** **oscillations** to median nerve stimulation in Patient 5. (A) Typical high-**frequency** **oscillation** potential recorded at electrode A5. (B) The location of recording electrodes. (C) Cortical distributions of the SEPs and high-**frequency** **oscillations**. P20/N20 are distributed diffusely around the primary hand sensorimotor area, while P25 is elicited in a restricted cortical area. Most **oscillation** potentials show a cortical distribution similar to that of P20/N20. Two later **oscillations** (n21 and p22) are elicited in a restricted cortical area similar to P25.
... Typical examples of high-**frequency** **oscillations** to median nerve stimulation recorded with a restricted bandpass filter of 500–2000 Hz compared with SEPs recorded with a wide bandpass filter of 30–2000 Hz. The SEPs and high-**frequency** **oscillations** were recorded at the same precentral electrodes (A1 in Patient 2 and A5 in Patient 5). Note the better isolated **oscillation** potentials on restricted filtering as a result of the attenuation of slower SEP components. Most of the **oscillation** potentials can be identified with both bandpass filters. p22 can only be seen on restricted bandpass filtering in Patient 2. The latencies of **oscillations** differed by 0.11 ms for the two different bandpass filters.
... Clinical and imaging characteristics of 8 patients for whom high-**frequency** **oscillations** were evaluateda
... Cortical distributions of SEPs and high-**frequency** **oscillations** to median nerve stimulation in Patient 7. (A) Typical high-**frequency** **oscillation** potential recorded at electrode C1. (B) The location of recording electrodes on the 3-dimensional MRI reconstruction. (C) Cortical distributions of the SEPs and high-**frequency** **oscillations**. Most **oscillation** potentials are distributed similar to or more diffusely than P20/N20. Three later **oscillations** (n18, p18 and n19) are elicited in a restricted cortical area similar to P25.
... High-**frequency** **oscillation**... Objective: To elucidate the generator sources of high-**frequency** **oscillations** of somatosensory evoked potentials (SEPs), we recorded somatosensory evoked high-**frequency** **oscillations** directly from the human cerebral cortex.... The locations of the subdural electrode array and functional brain mapping in each patient. SEPs and high-**frequency** **oscillations** were recorded from the electrodes enclosed by solid lines. Electrodes A7 and C4, and A4 were not used for recording because of disconnection of the wires in Patients 5 and 7, respectively. CS, central sulcus.

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In this paper, a new method for computing the amplitude and **frequency** of differential ring **oscillators** (ROs) is proposed. The analysis is performed in two separate parts. In the first of these, equations are derived with the assumption of a sinusoidal waveform of outputs, while in the other, the outputs are assumed to be exponential. It is shown that the derived equations for **frequency** and amplitude are sufficiently exact. In addition, conditions in which sinusoidal and exponential output occur are thoroughly discussed. In the instances in which the results did not satisfy the necessary conditions for sinusoidal output, the output is assumed to be exponential. Moreover, the related analytical equations are written, and the new expressions for **frequency** and amplitude of ROs are derived. Analytical results are confirmed by simulation results, using the Taiwan Semiconductor Manufacturing Company 0.18µm technology model. The simulation results indicate the high level of accuracy of the proposed model.... Plot of **oscillation** **frequency** versus the number of stage for sinusoidal case. Vbias=0.7, Iss=[0.6_1mA], Wn/L=7/0.18, Wp/L=10/0.18.
... Plot of **oscillation** **frequency** versus resistor load for sinusoidal case. N=3, Wn/L=[4/0.18_10/0.18], Cl=[67.5fF_87fF], Iss=1mA.
... The chain of delay stages in (a) a single-ended ring **oscillator** and (b) a differential ring **oscillator**.
... Ring **oscillators**... Plot of **oscillation** **frequency** versus the number of stage for exponential case. Vbias=0.7, Iss=[0.6_1mA], Wn/L=15/0.18, Wp/L=10/0.18.
... Plot of **oscillation** **frequency** versus external capacitor for exponential case. N=3, Wn/L=15/0.18, RL=1.5k, Iss=1mA.

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Sinusoidal **oscillator**... In this paper, two new designs are proposed for sinusoidal **oscillators** based on a single differential voltage current conveyor transconductance amplifier (DVCCTA). Each of the proposed circuits comprises a DVCCTA combined with passive components that simultaneously provides both voltage and current outputs. The first circuit is a DVCCTA-based single-resistance-controlled **oscillator** (SRCO) that provides independent control of the **oscillation** condition and **oscillation** **frequency** by using distinct circuit parameters. The second circuit is a DVCCTA-based variable **frequency** **oscillator** (VFO) that can provide independent control of the **oscillation** **frequency** by adjusting the bias current of the DVCCTA. In this paper, the DVCCTA and relevant formulations of the proposed **oscillator** circuits are first introduced, followed by the non-ideal effects, sensitivity analyses, **frequency** stability discussions, and design considerations. After using the 0.35-μm CMOS technology of the Taiwan Semiconductor Manufacturing Company (TSMC), the HSPICE simulation results confirmed the feasibility of the proposed **oscillator** circuits.... Simulation results of the start-up **oscillations** of the variable **frequency** dual-mode sinusoidal **oscillator** (Fig. 4).
... Circuit diagram of the proposed DVCCTA-based variable **frequency** dual-mode sinusoidal **oscillator**.
... Variation of the **oscillation** **frequency** against R2 for the circuit (Fig. 3).
... Simulation results of the highest applicable **oscillations** of the variable **frequency** dual-mode sinusoidal **oscillator** (Fig. 4): (a) output waveform in the steady state; and (b) the start-up of the **oscillations**.
... **Oscillation** **frequency** against the bias current IB of the circuit shown in Fig. 4.

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Sectorial **oscillation** of acoustically levitated water drop: (a) δ and ε versus time, (b) fit of outline with Eq. (2). δ and ε are the instantaneous amplitude of the axisymmetric **oscillation** and sectorial **oscillation** respectively.
... Sectorial **oscillation** **frequencies** and the corresponding modulation **frequencies** of levitated drops for degree l=2.
... Liquid drops can be suspended in air with acoustic levitation method. When the sound pressure is periodically modulated, the levitated drop is usually forced into an axisymmetric **oscillation**. However, a transition from axisymmetric **oscillation** into sectorial **oscillation** occurs when the modulation **frequency** approaches some specific values. The **frequency** of the sectorial **oscillation** is almost exactly half of the modulation **frequency**. It is demonstrated that this transition is induced by the parametric resonance of levitated drop. The natural **frequency** of sectorial **oscillation** is found to decrease with the increase of drop distortion extent.... Sectorial **oscillation** **frequency** of acoustically levitated water drops: (a) the angular **frequency** ω versus the equatorial radius a, (b) the decrease of ω with the increase of distortion extent a/r0. r0 is the radius of drop when it takes a spherical shape.
... Forced axisymmetric **oscillation** of acoustically levitated water drop: (a) bottom view images of the drop, (b) the time evolution of the equatorial radius R.
... Drop **oscillation**

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