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Amplitude and Intertrial Phase Coherence of Theta and Gamma **Oscillations**
... theta **oscillations**... The amplitude of stimulus-driven gamma **oscillations** is modulated by the phase of ongoing theta **oscillations**. This cross-**frequency** coupling indicates a hierarchical organization of cortical oscillatory dynamics in both healthy control subjects (black line) and schizophrenia patients (red line). The x axis indicates theta phase. The y axis indicates gamma amplitude.
... Heuristic model of phase-amplitude cross-**frequency** coupling. Gamma **oscillations** (red and blue lines) are largest in the excitatory versus inhibitory phase of ongoing theta **oscillations** (black line). Note that excitatory and inhibitory phase may vary according to tasks and neural sources.
... cross-**frequency** coupling... gamma **oscillations**... Schizophrenia patients have normal theta-phase/gamma-amplitude cross-**frequency** coupling. The modulation index demonstrates the relative strength of cross-**frequency** coupling via comparison of observed (O) versus resampled or surrogate (S) electroencephalography data in healthy control subjects (black circle) and schizophrenia patients (red squares). The y axis indicates log transform of modulation index.
... neural **oscillations**... Schizophrenia patients (SZ) have increased theta amplitude and decreased gamma synchrony. The left column shows time-**frequency** maps from healthy control subjects (HC) and the middle column shows time-**frequency** maps from schizophrenia patients. The x axis indicates time in milliseconds and the y axis indicates **frequency**. Color indicates amplitude in the top row and intertrial phase coherence (ITC) in the bottom row. The right column shows difference between schizophrenia patients and healthy control subjects. Difference maps show only time-**frequency** points at p < .01.

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Detection and parameters of ictal high **frequency** **oscillations** in 19 patients.
... Ictal EEG and HFO in Patient 1. (A) Conventional EEG (low-pass filter 120Hz, time constant 0.1s) reveals periodic sharp waves at LH1-3. The periodic sharp waves are followed by more repetitive sharp waves in the left hippocampus and amygdala. Filled circles indicate the presence of HFO. (B) HFO waveforms (low-pass filter 300Hz, time constant 0.003s). 200–250Hz high **frequency** activities are detected at LH1-3. Note the calibration, which shows that HFO waves have very small amplitude and short duration.
... Ictal EEG and HFO in Patient 2. (A) On conventional EEG (low-pass filter 120Hz, time constant 0.1s), ictal EEG starts with repetitive spikes at LA1, LH2, LH3, and LH4, as well as rhythmic alpha activity at LH1 at the same time. The spikes spread widely in the left temporal area, and are replaced by rhythmic beta waves at LH1, LH2, LH3, and LH4. The right hemispheric electrodes do not show clear ictal activities throughout. Filled circles and bold line indicate the presence of HFO. (B) HFO waveforms before conventional EEG onset, and around onset (low-pass filter 300Hz, time constant 0.003s). 200–333Hz high **frequency** activities are recorded at 1 to 3 electrodes on the right side (RA1, RH1, and RH2). Circles indicate the locations of HFO. Although spikes are seen on the left side, HFO is not recorded at the left-sided electrodes.
... Ictal EEG and HFO in Patient 7. (A) On conventional EEG (low-pass filter 120Hz, time constant 0.1s), ictal EEG starts with a large positive sharp wave at RH1 and RH2, followed by beta activities at the same electrodes. Seven seconds later, rhythmic beta waves start at RA1 and RA2 with gradual evolution. Approximately 45s later, left-sided electrodes (LH1-4 and LA1-4) start showing small spikes, followed by beta activities in the same electrodes Filled circles and the bold line indicate the presence of HFO. (B) HFO waveforms before conventional EEG onset, around onset, and around conventional EEG onset at the left hemisphere (low-pass filter 300Hz, time constant 0.003s). These demonstrate 200–333Hz high-**frequency** activities at 1–4 electrodes in the right side (RA1, RA2, RH1 and RH2). These also demonstrate high-**frequency** activities at LA1-2 and LH1 around the conventional EEG onset on the left side. Circles indicate the locations of HFO.
... High **frequency** **oscillations**... Detection and parameters of interictal high **frequency** **oscillations**.

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Pressure fluctuations in the 8-in. burner for the stable combustion case ((A), Φ=0.7) and for the **oscillating** case ((B), Φ=1.0) under the fixed air flow rate condition Qa=800m3/h.
... Pressure fluctuations spectra of the 12-in. burner for the stable combustion case ((A), part (a) of Fig. 11A), and for the **oscillating** case ((B), part (a) of Fig. 11B), and for the early stage of the high **frequency** **oscillation** ((C), part (b) of Fig. 11B).
... Pressure fluctuations spectra of the 8-in. burner for the stable combustion case ((A), part (a) of Fig. 8A), and for the **oscillating** case ((B), part (a) of Fig. 8B), and for the early stage of the high **frequency** **oscillation** ((C), part (b) of Fig. 8B).
... Natural **frequencies** of tangential/radial mode **oscillations** of the 12-in. burner (A) and the experimental peak **frequencies** (B) (peak **frequencies** (c)–(h) in Fig 12B).
... Natural **frequencies** of tangential/radial mode **oscillations** of the 8-in. burner (A) and the experimental peak **frequencies** (B) (peak **frequencies** (c)–(h) in Fig 10B).

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Representative time-**frequency** spectra and the corresponding electroencephalography (EEG) traces. Parts of the temporally expanded and filtered EEG traces are shown in the left column (low-cut filtered at 0.5Hz in blue and filtered at 70Hz in red). A ripple with a **frequency** above 100Hz occurs in temporal association with the positive peak, the ascending slope, and/or the negative peak of the spike; it is barely visible near the spike-peak in the trace with a 0.5-Hz filter (magnification in box). The resulting time-**frequency** spectra in the right column show spectral spots (yellow arrows) in association with the spikes in the overlaid traces from the EEGs with CSWS (B corresponding to A with a peak **frequency** of 128.9Hz; (D) corresponding to (C) with a peak **frequency** of 125.0Hz).
... Ictal discharges associated with epileptic spasms. (A) Ictal ECoG traces are shown with a low-**frequency** filter of 53Hz and a high-**frequency** filter of 300Hz. Ictal augmentation of HFOs occurred at channel 1 and quickly involved the surrounding channels. The end of HFOs augmentation occurred at channel 1 and sequentially involved the surrounding channels; this observation was referred to as the “ictal doughnut phenomenon”. The trigger point for time-**frequency** analysis was placed at the EMG onset detected at right deltoid muscles. (B) Time-**frequency** plots derived from 62 spasms are shown. Augmentation of HFOs preceded the EMG onset (denoted as ±0ms). (C) The amplitudes of HFOs associated with spasms are shown.
... Ripples recorded with surface EEG. Example of ripples recorded on surface EEG. The upper section shows ripple **oscillations** co-occurring with a spike, with **oscillations** visible during the spike. The middle section shows a ripple co-occurring with a spike with **oscillations** not visible during the spike, but visible after filtering. In the bottom section a ripple independent of any spike can be observed. (A) Raw EEG. (B) Raw EEG with expanded time. (C) EEG filtered with high-pass filter of 80Hz.

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Time-**frequency** analysis... Multivariate modulated **oscillations**... The partitioned **frequency** domain with the multivariate bandwidth given by Bl,m, where l corresponds to the level of the **frequency** band and m is the **frequency** band index.
... Time-**frequency** analysis of Doppler radar data. (a) The time domain waveforms of both the high gain and low gain Doppler radar data. (b) The time-**frequency** representation of Doppler radar data using the proposed multivariate extension of the SST (left panel) and the MPWD algorithm (right panel). A window length 1063 was used for the MPWD.
... Amplitude and **frequency** modulated signal... Instantaneous **frequency**... The time-**frequency** representations for both the proposed method (left panels) and the MWPD (right panels) for a bivariate AM/FM signal, with input SNR of (a) 10dB, (b) 5dB and (c) 0dB. The window length used for MPWD was 681 samples.
... Time-**frequency** analysis of real world float drift data. (a) The time domain waveforms of bivariate float velocity data. (b) The time-**frequency** representation of float data using the proposed multivariate extension of the SST (left panel) and the MPWD algorithm (right panel). A window length 501 was used for the MPWD.
... A comparison between the localization ratios B, for both the proposed method and the MPWD, evaluated for a bivariate **oscillation** with the following joint instantaneous **frequencies**: (a) 10.5Hz, (b) 40.5Hz, and (c) 100.5Hz. A window length of 1001 samples was used for the MPWD.

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Microbubble **oscillation**... The bubble’s natural **frequency** as a function of bubble radius for bubbles lying in the center of compliable vessels with L = 100 μm: (a) dimensional natural **frequency**; (b) dimensionless natural **frequency**.
... Natural **frequency**... The natural **frequency** of a bubble with a0 = 4 μm as a function of the rigidity index k of the blood vessel in compliable vessel with R0 = 5 μm and L = 500 μm: (a) dimensional natural **frequency**; (b) dimensionless natural **frequency**.
... The bubble’s natural **frequency** as a function of the vessel inner radius for bubbles lying in the center of compliable vessels with L = 100 μm: (a) dimensional natural **frequency**; (b) dimensionless natural **frequency**.
... The bubble’s natural **frequency** as a function of bubble radius for bubbles lying in the center of rigid vessels with L = 500 μm: (a) dimensional natural **frequency**; (b) dimensionless natural **frequency**.
... The bubble’s natural **frequency** as a function of the vessel inner radius for bubbles lying in the center of rigid vessels with L = 500 μm: (a) dimensional natural **frequency**; (b) dimensionless natural **frequency**, which is the normalized natural **frequency** of a bubble in the corresponding unbounded field predicted by the Rayleigh-Plesset equation f0=12π3κ(p0+2σ/a0)ρa0 2 − 2σρa0 3.
... Nonlinear **oscillation**

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When analyzing the nonlinear Duffing **oscillator**, the weak nonlinearity is basically dependent on the amplitude range of the input excitation. The nonlinear differential equation models of such nonlinear **oscillators**, which can be transformed into the **frequency** domain, can generally only provide Volterra modeling and analysis in the **frequency**-domain over a fraction of the entire framework of weak nonlinearity. When the amplitude of the excitation exceeds a certain value, the underlying nonlinear differential equation will become invalid in the **frequency** domain. This paper discusses the problem of using a new non-parametric routine to extend the capability of Volterra analysis, in the **frequency** domain, to weakly nonlinear Duffing systems at a much wider range of excitation amplitude range which the current underlying nonlinear differential equation models fail to address.

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Dependency of the computed **oscillator** parameters as a function of the normalized **frequency**.
... Variations of the computed self-starting **oscillations** **frequency** versus normalized s parameter.
... Dependence of the amplitude and **frequency** of **oscillations** on bias voltage for the first stage of the **oscillator**.
... Variation of **frequency** and amplitude of **oscillations** on the load resistor for the circuit **oscillator** with single TD.
... Self-starting **oscillation**... Variations of the amplitude and **frequency** of **oscillations** as a function of external capacitor values, and positions.
... Millimeter wave **oscillators**... Cascaded **oscillator** networks

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