Frequency Modulation Research Articles

Approximate analytic solution of the dissipative semiclassical Rabi model under parametric multi-tone modulations

Abstract We present an analytic method for obtaining the dynamics of the dissipative time-modulated
semiclassical Rabi model, which describes a two-level system (qubit) with time-dependent parameters, 
coupled to a single-mode bosonic field via the dipole-interaction and to
a thermal reservoir. We consider the simultaneous harmonic
modulations of the qubit transition frequency and the qubit-field coupling strength,
with arbitrary frequencies, and obtain closed analytic expressions for the
density operator under the coarse-graining approximation. Our
approximate results are in excellent ageement with exact numerical data, and
illustrate how the qubit state can be controlled in the dispersive regime by properly
adjusting the system parameters.

Comprehensive investigation of novel synthesized thiophenytoin derivative (antiepileptic drug) as an environmentally friendly corrosion inhibitor for mild steel in 1 M HCl: Theoretical, electrochemical, and surface analysis perspectives

This study evaluates the potential of N-(2,6-dimethylphenyl)-2-(5-oxo-4,4-diphenyl-4,5-dihydro-1H-imidazol-2-yl)thio)acetamide (AM16), a novel thiophenytoin derivative used as an antiepileptic drug, as a corrosion inhibitor for mild steel in 1.0 M HCl. The research focuses on AM16’s adsorption behavior and corrosion inhibition efficiency. Electrochemical techniques, including potentiodynamic polarization (PDP), electrochemical impedance spectroscopy (EIS), and electrochemical frequency modulation (EFM), were employed to assess the inhibitor’s effectiveness. The results demonstrate that AM16 achieved a corrosion inhibition efficiency of 95.7 %, with its performance improving with increasing concentration. Polarization studies reveal that AM16 acts as a mixed-type inhibitor. The adsorption of AM16 on the steel surface was modeled using the Langmuir adsorption isotherm. Surface analysis via scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), and X-ray photoelectron spectroscopy (XPS) confirmed the formation of a protective layer. Experimental findings were complemented by density functional theory (DFT)-based calculations. The combined theoretical, experimental, and analytical approaches affirm the efficacy of this molecule as a corrosion inhibitor, achieving a 95.7 % inhibition rate. Polarization studies reveal that the inhibitor acts as a mixed-type inhibitor. Thermodynamic parameters suggest that the molecule chemically adsorbs onto the steel surface, following the Langmuir isotherm.

LPI radar waveform design based on complementary phase and discrete chaotic frequency joint coding

In order to reduce the probability of radar radiation signals being detected by enemy passive detection systems, this paper proposes a phase and frequency joint coding low intercept Radar waveform design method. Based on the linear frequency modulation signal, this method uses complementary binary code and chaotic sequence to phase encode the intra-pulse modulation. Code and frequency coding. The numerical simulation results show that the designed waveform exhibits pseudo-random characteristics in the time-frequency domain, and the low recognition performance is improved; The signal has an extremely low peak sidelobe level after matched filtering, showing excellent low intercept performance; its three-dimensional ambiguity function diagram presents an ideal “graph”. Fishing type”, with good distance, speed resolution and anti-interference characteristics.

Microwave Coincidence Imaging with Phase-Coded Stochastic Radiation Field

Microwave coincidence imaging (MCI) represents a novel forward-looking radar imaging method with high-resolution capabilities. Most MCI methods rely on random frequency modulation to generate stochastic radiation fields, which introduces the complexity of radar systems and imposes limitations on imaging quality under noisy conditions. In this paper, microwave coincidence imaging with phase-coded stochastic radiation fields is proposed, which generates spatio-temporally uncorrelated stochastic radiation fields with phase coding. Firstly, the radiation field characteristics are analyzed, and the coding sequences are designed. Then, pulse compression is applied to achieve a one-dimensional range image. Furthermore, an azimuthal imaging model is built, and a reference matrix is derived from the frequency domain. Finally, sparse Bayesian learning (SBL) and alternating direction method of multipliers (ADMM)-based total variation are implemented to reconstruct targets. The methods have better imaging performance at low signal-to-noise ratios (SNRs), as shown by the imaging results and mean square error (MSE) curves. In addition, compared with the SBL and ADMM-based total variation methods based on the direct frequency-domain solution, the proposed method’s computational complexity is reduced, giving it great potential in forward-looking high-resolution scenarios, such as autonomous obstacle avoidance with vehicle-mounted radar and terminal guidance.

State-space analysis of a continuous gravitational wave source with a pulsar timing array: inclusion of the pulsar terms

ABSTRACT Pulsar timing arrays (PTA) can detect continuous nanohertz gravitational waves (GW) emitted by individual supermassive black hole binaries. The data analysis procedure can be formulated within a time-domain, state-space framework, in which the radio timing observations are related to a temporal sequence of latent states, namely the intrinsic pulsar spin frequency. The achromatic wandering of the pulsar spin frequency is tracked using a Kalman filter concurrently with the pulse frequency modulation induced by a GW from a single source. The modulation is the sum of terms proportional to the GW strain at the Earth and at every pulsar in the array. Here, we generalize previous state-space formulations of the PTA problem to include the pulsar terms; that is, we copy the pulsar terms from traditional, non-state-space analyses over to the state-space framework. The performance of the generalized Kalman filter is tested using astrophysically representative software injections in Gaussian measurement noise. It is shown that including the pulsar terms corrects for previously identified biases in the parameter estimates (especially the sky position of the source) which also arise in traditional matched-filter analyses that exclude the pulsar terms. Additionally, including the pulsar terms decreases the minimum detectable strain by 14 per cent. Overall, the study verifies that the pulsar terms do not raise any special extra impediments for the state-space framework, beyond those studied in traditional analyses. The inspiral-driven evolution of the wave frequency at the Earth and at the retarded time at every pulsar in the array is also investigated.

A Parameter-Adaptive Method for Primary Frequency Regulation of Grid-Forming Direct-Drive Wind Turbines

When wind turbines contribute to system frequency support using virtual synchronous generator (VSG) control, conventional VSG methods often fall short of meeting operational demands, particularly in terms of inertia and frequency support. In this study, considering both the frequency regulation and dynamic performance of VSG, a novel parameter design method that enhances frequency modulation capabilities is proposed in this paper. Initially, VSG control is integrated into the grid-side converter of a direct-drive permanent magnet synchronous generator (D-DPMSG) wind turbine. A small-signal model of the D-DPMSG-VSG active power is then formulated to analyze how the moment of inertia and damping coefficient impact system stability. Subsequently, ensuring that system parameter constraints are met, the key parameters of VSG are adaptively designed to dynamically adjust the system’s frequency and output power during transient responses. Finally, simulation results based on D-DPMSG-VSG in MATLAB/Simulink validated the feasibility, effectiveness, and advantages of the proposed parameter-adaptive VSG control strategy for enhancing the frequency modulation (FM) performance of wind turbines.

Quantification of nonlinear effect in seismic signal using Holo-Hilbert spectral analysis

Affected by excitation conditions, absorption, and attenuation of stratum and receiving instruments, the seismic signal is non-stationary and nonlinear. Time-frequency spectral analysis methods are effective and widely used in describing the time-varying features of seismic signals. However, these methods are all based on additive expansions, and cannot represent the nonlinearity of signal, which is achieved through a multiplicative process. Therefore, the information provided by the time-frequency spectrum is incomplete. To show the nonlinearity of seismic signal, that is, the modulation effect of low-frequency components on high-frequency components, the Holo-Hilbert spectral analysis method is introduced in this paper. Holo-Hilbert spectral analysis (HHSA) contains nested empirical mode decomposition and Hilbert transform to achieve a full informational spectrum represented by two frequency dimensions. In the Holo-Hilbert spectrum, one dimension represents frequency-modulated (FM) frequency, which characterizes the non-stationarity of the signal, and the other dimension represents the amplitude-modulated (AM) frequency, which indicates the nonlinear effect in the signal. Synthetic and field data examples verify the feasibility of HHSA in characterizing the cross-frequency interaction of non-stationary seismic signals as a potential tool to detect reservoirs.

Multi-source Frequency Modulation Optimization Strategy Based on Multi-objective Two-Layer Game

Multi-source Frequency Modulation Optimization Strategy Based on Multi-objective Two-Layer Game

Real‐Time Force Monitoring of Electrically Stimulated 3D‐Bioengineered Muscle Bioactuators Using Organic Sensors with Tunable Sensitivity

The contractile nature of skeletal muscle tissue makes it especially attractive for powering biohybrid actuators. Significant efforts have been dedicated to the improvement and control of contraction force, going one step forward toward the automation of these biohybrid platforms. Herein, 3D‐bioengineered skeletal muscle tissues are integrated with organic transistor‐based sensors to define a soft bioactuator with real‐time force monitoring capabilities. The muscle tissue is electrically stimulated while the organic sensor ensures transduction of the exerted force into an electrical signal that allows direct monitoring of the bioactuator performance. Sensor calibration is carried out to define its sensitivity at different biasing conditions: as opposed to standard, two‐terminal piezoresistive devices, transistor‐based strain sensors show tunable sensitivity by acting on the voltage applied to a third terminal—the gate. A complete evaluation of sensing performances is provided, demonstrating that real‐time monitoring is effective under different conditions, including stimulation signal frequency and chemical modulation of the bioactuator contraction, demonstrating its potential use as a drug testing platform. In the reported results, the way is paved for a complete exploitation of organic devices in soft robotic applications and to the development of novel biohybrid machines in bioengineering and biomedicine.

Enhancing distribution system stability and efficiency through multi‐power supply startup optimization for new energy integration

AbstractThis paper addresses the challenge of maximizing power capture from new energy sources, including coal, wind, solar, and hydroelectric power, which often lack sufficient inertia support. This deficiency can lead to frequency instability and cascading failures within the power system. A cooperative optimization model for the start‐up of multiple power supplies, designed to enhance the integration of new energy sources while maintaining system stability is proposed. The model incorporates primary frequency modulation and the intrinsic inertia support capabilities of self‐synchronous voltage source field stations, considering dynamic frequency constraints. Additionally, it employs new energy units with primary frequency modulation to provide inertia support during curtailment, particularly when conventional units cannot meet frequency standards due to existing constraints. Extensive simulations and comparative analyses demonstrate that the proposed model improves new energy utilization by up to 37.5% and reduces operational costs by approximately 16%, enhancing overall operational efficiency in high energy consumption scenarios.

Comparison of space vector and switching frequency optimal pulse width modulation for diode free F‐type multi level inverter

AbstractThis study presents a comprehensive examination of space vector pulse width modulation (SVPWM) and switching frequency optimal PWM (SFOPWM) for an F‐type multilevel inverter (FTMLI). SVPWM offers a simple, digital implementation for three‐phase, three‐level inverter structures, and carrier‐based SFOPWM allows for maximum use of switching frequency with a simple construction. This approach reveals the underlying relationship between the above two PWM techniques with various amplitude and frequency modulation indices to ensure the performance of FTMLI. A suitable comparative study was carried out to verify the PWM techniques based on the inverter output voltage, total harmonic distortion, switching stress, and filter size. The analytical conclusions are supported by the simulation results and their experimental validation.

Detecting optical frequency in weak signal light using injection-induced frequency modulation

In fiber-optic sensing, long-distance transmission and demodulation of weak signal light (SL) are critical. This study improves the system by relocating an external cavity tunable laser (ECTL) to the transmission end. Directly injecting the SL into the ECTL modulates the output light and uses the high-power ECTL light for transmission, reducing loss. At the demodulation end, an orthogonal Mach-Zehnder interferometer (MZI) and an H13C14N gas absorption cell (GAC) extract SL wavelength information. Results demonstrate effective modulation with SL intensity as low as 1 nW and a demodulation resolution of up to 10 MHz, offering significant improvements in long-distance fiber-optic sensing.

Wideband FMCW radar for long-distance target detection based on photonic chirp pulse stitching.

Current wideband frequency-modulated continuous-wave (FMCW) radar fails in detecting long-distance target, since only the target whose echo is temporally close to the reference linear frequency modulation (LFM) chirp can be detected. We propose a long-distance target detection method for the wideband FMCW radar based on photonic chirp pulse stitching. The stitching photonic chirp pulse that is generated through optical up- and downconversion of the LFM is employed as local signal for the de-chirping process instead of the LFM itself, as currently used. By adjusting the transmitting signal period, a theoretically arbitrarily large detection distance can be obtained with the proposed method. Experiments obtain high-resolution range profiles for two targets located at 1.44 km and 14.5 km, respectively, proving the feasibility of the proposed scheme.

Magnetospheric Line Radiation: Temporal Modulation Corresponding to a Bouncing Wave

AbstractMagnetospheric line radiation (MLR) is a peculiar type of whistler‐mode emissions formed by several similarly spaced spectral lines, whose frequencies may vary with time. These emissions typically occur at frequencies between about 1 and 8 kHz and are observed in both ground‐based and satellite measurements. However, their origin and source locations are not yet understood, as their detection by spacecraft instruments is challenging due to the limited frequency resolution of onboard wave measurements. We use high‐resolution multicomponent wave data obtained by the Van Allen Probes to demonstrate that, in addition to the frequency modulation, MLR events possess a temporal modulation with periods on the order of seconds, which may be related to the wave bouncing between hemispheres. Observed modulation periods are used to estimate a tentative source L‐shell. The modulation periods are shorter for events with larger frequency spacing, and the estimated source L‐shells correlate with model plasmapause locations.

Experimental study on sound propagation caused by disturbance of wake flow on water surface boat

The research on underwater sound propagation generally assumes that the water is static. However, when a boat passes on the water surface, its wake can cause disturbance to the stable sound field. The main reason is that the wake changes the temperature and salinity distributions of seawater in the just field, thereby affecting propagation loss. This article conducts a time-frequency analysis of the sound signal propagated by the boat wake. Results show that the wake not only affects the propagation loss but also causes obvious fluctuations in the envelope of the received signal. This fluctuation indicates the frequency modulation of sound by the boat wake. These changes in sound propagation are not only related to the boat speed but also to the signal frequency.

Quantifying the frequency modulation in electrograms during simulated atrial fibrillation in 2D domains

Atrial fibrillation (AF) affects millions of people in the world, causing increased morbidity and mortality. Treatment involves antiarrhythmic drugs and catheter ablation, showing high success for paroxysmal AF but challenges for persistent AF. Experimental evidence suggests reentrant waves and rotors contribute to AF substrates. Ablation procedures rely on electroanatomical maps and electrogram (EGM) signals; however, current methods used in clinical practice lack consideration for time–frequency varying EGM components. The fractional Fourier transform (FrFT) can be adopted to capture time-varying frequency components, thereby enhancing the comprehension of arrhythmogenic substrates during AF for improved ablation strategies. To this end, a FrFT-based algorithm is developed to characterize non-stationary components in EGM signals from simulated AF episodes. The proposed algorithm comprises a pre-processing step to enhance the coarser features of the EGM waveform, a windowing process for dynamic assessment of the EGM, and a FrFT order optimization stage that seeks compact signal representations in fractional Fourier domains. The resulting order is related to the rate of frequency change in the signal, making it a useful indicator for frequency-modulated components. The FrFT-based algorithm is implemented on EGM signals from AF simulations in 2D domains representing a region of the atrial tissue. Consequently, the computed optimum FrFT orders are used to build maps that are spatially correlated to the underlying propagation dynamics of the simulated AF episode. The results evince that the extreme values in the optimum orders map pinpoint the localization of fibrillatory mechanisms, generating EGM activation waveforms with varying frequency content over time.

Broadband multi‐carrier linear frequency modulation signal reception with subcarrier frequency offset deramp processing

AbstractIn this paper, a broadband multi‐carrier linear frequency modulation (LFM) signal reception method with subcarrier frequency offset deramp processing is proposed and investigated. The proposed frequency offset deramp processing is implemented by mixing the multi‐carrier LFM radar echo with a multi‐carrier LFM reference that has a different subcarrier frequency interval. With this design, the sampling rate of the radar receiver is remarkably reduced and crosstalk‐free separation of different subcarrier signals is easily conducted in the frequency domain. To fuse the multiple subcarriers and fill the frequency gaps, a sparse reconstruction method is employed to obtain the broadband response, which is essential for achieving high range resolution detection. The effectiveness of the proposed method is validated through an experiment in which the reception of an 8‐carrier LFM signal is conducted and a total bandwidth of 6 GHz after multi‐carrier fusion is demonstrated. An inverse synthetic aperture radar imaging experiment is also conducted with the results verifying the good potential of the proposed method in practical applications.

Frequency linearization of voltage controlled oscillator (VCO) for 2 µs frequency modulated continuous wave (FMCW) reflectometer.

Frequency modulated continuous wave reflectometers have been widely used to measure plasma density profiles in many magnetic fusion devices. The frequency modulation (FM) time of the KSTAR reflectometer was 20 µs, that is, the FM rate was 50kHz. However, the edge density of the KSTAR tokamak fluctuates typically over the frequency range of 20-50kHz in the ELMy H-mode plasmas. Therefore, the density profile changes significantly during the FM time, causing significant distortion in the density profile measurements. The FM rate must be increased at least ten times faster than the density fluctuation frequency. A new voltage controlled oscillator (VCO) driver is designed based on the AD8067 operational amplifier to achieve a FM time of 2 µs. The VCO output frequency is linearly modulated by predistorting the tuning voltage of VCO using a 400 MSamples/s arbitrary waveform generator. The resulting output frequency of the VCO is measured by mixing the VCO output with a fixed frequency synthesizer signal and measuring the mixer intermediate frequency using a 2.5 GSamples/s digitizer. The tuning voltage is adjusted to minimize the amount by which the measured frequency deviates from the linearly modulated frequency. A simple linear adjustment proportional to the deviation does not effectively suppress the nonlinearity in FM. The response time of the VCO driver and the VCO input interface should be taken into account by solving the entire circuit equation. In this paper, the developed VCO driver circuit and the frequency linearization method are described.

Algorithm for Designing Waveforms Similar to Linear Frequency Modulation Using Polyphase-Coded Frequency Modulation

Linear frequency modulation (LFM) waveforms have been widely adopted due to their excellent performance characteristics, such as good Doppler tolerance and ease of physical implementation. However, LFM waveforms suffer from high autocorrelation sidelobes (ACSLs) and limited design flexibility. Phase-coded frequency modulation (PCFM) waveforms can be used to design waveforms similar to LFM, offering greater design flexibility to optimize ACSLs. However, it has been found that the initial PCFM waveform experiences spectral expansion during the ACSL optimization process, which reduces its similarity to LFM. Therefore, this article jointly optimizes the ACSLs and spectrum of the initial PCFM waveform, establishes an optimized mathematical model, and then solves it using the heavy-ball gradient descent algorithm. Numerical experiments indicate that the proposed method effectively addresses the problem of waveform similarity degradation caused by spectral expansion while reducing waveform ACSLs. At the same time, a balance between reducing waveform ACSLs and preserving waveform similarity can be achieved by adjusting the parameters.

Two-dimensional viscous study of coupled nonlinear fluid resonances in two narrow gaps

The wave-induced hydrodynamics of coupled nonlinear piston-mode fluid resonances within two narrow gaps between three barges are numerically investigated using a two-dimensional viscous wave flume. This study aims to explore the time-dependent nonlinear interactions between fluid oscillations in the two gaps. The coupled synchronous dynamic behaviors of fluid oscillations during the transient evolution stage are first examined in terms of amplitude and frequency modulation. It is shown that phase dynamics, including phase slipping, trapping, and locking, play significant roles in establishing the coupled synchronous dynamic evolutions of fluid oscillations in the two gaps. The quasi-steady state of the amplitude- and phase-frequency responses of fluid oscillations within the gaps, along with the reflection and transmission waves in front of and behind the three-barge system, are further analyzed. This analysis clarifies the significance of viscous damping energy dissipation and radiation damping energy transfer involved in gap resonance problems. This clarification also explains the performance of fully nonlinear potential flow solvers in predicting fluid resonances in the two narrow gaps. Finally, the nonlinear dynamic features of fluid oscillations are examined. The effects of incident wave nonlinearity, i.e., wave steepness, on resonant frequencies, response amplitudes, energy dissipation, and reflection and transmission coefficients are investigated. Harmonic analysis via Fourier transformation reveals the contributions of first-, second-, and third-order harmonics to the overall response amplitudes. The physical insights gained from this study provide a deeper understanding of the coupled nonlinear dynamics of piston-mode fluid resonances in multiple narrow gaps.