Fractional Frequency Research Articles

Phase demodulation method for stable long-haul frequency transmission based on the Michelson interferometer.

In this Letter, we present a fiber-optic radio frequency (RF) transmission scheme based on phase modulation with an interferometric detection structure. A self-developed Michelson interferometer (MI) is used to demodulate the frequency signal via an electrically controlled optical shifter. The two complementary outputs from the interferometer are detected using a balanced detector, which suppresses the common-mode noise of the fiber link. The structure is tested in the laboratory using a frequency transfer system over a 560 km fiber link. Experimental results show that a stable 2.4 GHz frequency transmission with a fractional frequency instability of 3.9 × 10-14 at 1 s and 6.2 × 10-17 at 10,000 s is achieved. Compared with the frequency transmission system based on intensity modulation and direct detection, the frequency instability is improved from 7.3 × 10-14 to 3.9 × 10-14 at 1 s. We believe that the proposed method will be useful for the construction of time-frequency synchronous fiber networks.

Characterisation and synchronisation of a netted software defined radio radar

AbstractThe present work intends to characterise the combination of two netted software defined radios (SDR) and different radio frequency (RF) front‐ends installed in them, together with a two‐stratum time dissemination and synchronisation system. A modified implementation of the Network Time Protocol is used as coarse event synchronisation for either SDR back‐end. The White rabbit light embedded node implementation of the commonly known white rabbit synchronisation system (IEEE 1588 PTP‐2019) or arbitrary wave form generators are used as fine time dissemination system for either SDR. The resulting netted transceiver system is intended to compose a demonstrator for proof‐of‐concept experiments. The findings presented in this article show that the chosen combination of hardware and software is suitable for radar applications operating within L‐, S‐ and C‐bands. A channel coherency throughout the network with a relative modified Allan deviation of less than 80 fs for averaging intervals of 1 s, a phase noise better than −118 dBc/Hz at 10 Hz frequency offset and a fractional frequency lower than was measured. Within a single transceiver node, a fractional frequency lower than and phase noise of −124 dBc/Hz at 10 Hz frequency offset were measured as well. Multistatic radar systems exploit wide spatial diversity to enhance target detection and tracking, albeit with increased complexity when compared to a monostatic configuration. To exploit these benefits, all participating transceiver nodes within the netted radar need to synchronise to a common time base . The achieved synchronisation level increases the accuracy with which the chain of timed events at the transmitter and at the receiver side occur, intending to maximise the signal‐to‐noise ratio available at the receiver. The Universal software radio peripheral model X310 with two different daughterboard models as RF front‐end was used as SDR on either radar node. A network combining data and synchronisation purposes allowed the radar nodes under test to operate synchronously. The two‐stratum synchronisation system used glass fibres between 2 m and 5 km of length or coaxial cables with 2 m in length for network traffic, time and frequency dissemination purposes. The multiple RF front‐ends were stimulated by means of arbitrary waveform generators with calibrated traceability. Up‐chirp and sinusoid waveforms were used as stimuli for measuring the offset of either channel with regards of to ultimately estimate the achievable coherency limits of the system under test. Both analogue and digital evaluation methods were considered.

Double Deep Q- energy aware Service allocation based on Dynamic fractional frequency reusable technique for lifetime maximization in HetNet-LTE network

The development of mobile communication in heterogeneous networks is incredible in providing various services through wireless cellular communication through advanced long-term evaluation networks. Increasing multi-concern services and frequencies in spectrum channels are highly layered to select the bandwidth to provide the fastest network without interference. Selecting the channel through macro cell selection is essential to improve network communication and provide the quickest service. Most frequency reuse techniques use service optimality and route selection-based protocols to enrich the packet flow. Still, the improper spectrum delights create more delay tolerance due to short-range service optimality due to energy loss by selecting the short spectrum signal to reuse, which doesn't support the lifetime improvement of the LTE network. To resolve these problems, we propose a Double Deep Q- energy-aware Service allocation based on a Dynamic fractional frequency reusable technique for lifetime maximization in the HetNet-LTE network. Initially, the heterogenous communication environment and node deplanement were carried out to construct the LTE network under the WCC. The communication logs are Route Table (RT), and its services are taken by all node LTE Communication Impact Rate (LTE-CIR). Then, the Backhaul Traffic Algorithm (BTA) is applied to predict the interference on traffic rate from the channel frequency margin. Select the balanced node using the Channel Interference Macro Cell Selection (CIMCS) technique. Considering frequency limits with the Double Deep Q- Network (DDQN) approach, energy-aware selects the optimal route to reuse the frequency level using Frequency Domain Packet Scheduling (FDPS) to improve communication. The proposed system improves the overall throughput by up to 97.8 % with adopted channel selection from the macro unit to improve the latency performance. Also, the interference frequency limits are dynamically reused at an energy optimal level with low-level delay tolerance to improve the link stability by up to 98.4 % with higher lifetime maximation in the LTE network.

Design and Implementation of Digital Integrated Circuit Based Frequency Dividers

This research aims to research the basic fractional frequency division. This article first introduces the theory of the dualmode prescaler method, and then use this method to calculate the number of integer frequency divisions and show that how to achieve the target fractional division ratio. after that, Verilog code is used to implement fractional frequency division, and using simulation to show the operation of the divider. The simulation shows that the designed fractional frequency divider can be implemented by evenly inserting different values of integer frequency dividers. However, the experiment in this article may has time error in the output signal, because the accurate 50% duty cycle cannot be achieved. In addition, the frequency division period is not completely uniform. Finally, the challenges and limitations of fractional frequency division technology in theory and practice will be summarized.

Anomalous Subkelvin Thermal Frequency Shifts of Ultranarrow Linewidth Solid State Emitters.

We investigate the frequency response of narrow spectral holes in a doped crystal structure as a function of temperature below 1K. We identify a particular regime in which this response significantly deviates from the expected two-phonon Raman scattering theory. Namely, near 290mK, we observed a behavior exhibiting a temperature-dependent frequency shift of zero to first order. This is of particular interest for applications that require high frequency stability, such as laser frequency stabilization, as by operating the scheme at this specific point would result in the spectral hole frequency being highly immune to temperature fluctuations, providing the potential for a laser fractional frequency instability as low as ∼2×10^{-22} at 1s.

Investigation on Dynamic Behaviors of Ship Propulsion Shafting with Misalignment Based on Stochastic Uncertainty Models

To investigate the effect of stochastic uncertainty on the dynamic behaviors of ship propulsion shafting with misalignment, a stochastic uncertainty model of ship shafting is established based on nonparametric theory and stochastic excitation. Numerical simulation and experimental verification of the dynamic behaviors are carried out using a ship shafting test bench. The results indicate that stochastic uncertainty has a significant effect on the dynamic behaviors of shafting with misalignment. With an increase in stochastic uncertainty, the fractional frequency appears in the spectrum, and the axis trajectory becomes more complex and gradually deviates from the center orbit. Therefore, to ensure the safe navigation of ships, it is necessary to consider the stochastic uncertainty in dynamic research on the misalignment of shafting.

Exploring Saudi Arabia’s 2060 net zero-emission paths via fractional frequency Fourier procedures. The imperatives of resource efficiency, energy efficiency, and digitalization

ABSTRACT By applying the novel fractional frequency Fourier ARDL technique, we unraveled the intricacies underpinning resource efficiency, energy efficiency, digitalization, and environmental sustainability in Saudi Arabia. Compelled by the conflicting narratives of prior investigations and the need for updated insights, the analyzed time series spanning 1990–2022 periods divulged interesting insights amenable to policy optimization. First, the fractional frequency Fourier ADL cointegration procedure reveals a long-term association among all the enlisted series. Second, resource and energy efficiencies, as well as digitalization, improved environmental quality by limiting carbon intensities and ecological footprint with some heterogeneous attributes across the timeframes. Notably, while resource efficiency is more effective toward ecological footprint mitigations, energy efficiency proves more efficient for carbon intensity reductions. Lastly, the fractional frequency Fourier Toda-Yamamoto causality test affirms the predictive attributes of the enlisted series on environmental performance. Hence, these factors are critical to KSA’s environmental sustainability paths. Based on these empirical discoveries, policymakers in KSA must pay adequate attention to the efficient utilization of resources and energy to complement other steps toward realizing Saudi Arabia’s 2060 net zero-emission. Likewise, policymakers must ensure the efficient allocation of income to environmentally sensitive ventures to curtail its negative repercussions on the environment. Other relevant steps to curtail carbon intensities and ecological footprint for optimal environmental performance in KSA have been highlighted.

Multiple-Access Time and Frequency Transfer over Fiber and Free-Space Link Based on Optical Frequency Comb

We have demonstrated a multiple-access transfer of time and frequency signal over a fiber and free-space link based on an optical frequency comb (OFC). With this transfer technique, two time–frequency signals were disseminated separately from a master site to two slave sites over a 3.9 km fiber and 100 m free-space link for 10,000 s. The timing fluctuations and instabilities of the time and frequency transfer were measured, estimated, and discussed. The experimental results show that the total root-mean-square (RMS) timing fluctuation of the transfer from site A to B is about 119 ps, with a fractional frequency instability on the order of 3.3 × 10−11 at 1 s and 2.8 × 10−14 at 2000 s. The RMS timing fluctuation of the transfer from site A to C is about 59.5 ps, with a fractional frequency instability on the order of 3.0 × 10−11 at 1 s and 2.6 × 10−14 at 2000 s. These results indicate that the multiple-access transfer technique proposed in this paper can provide important support for the application of a large-scale time–frequency synchronization network.

The Situation of Inflation Hysteresis in Türkiye: Analysis with Traditional, Fourier and Fractional Frequency Fourier Tests

This study investigates the impact of exchange rate shocks on pricing and whether the values normalise after the shock ends. Accordingly, the study tests the existence of inflation hysteresis. Goods and services sector inflation figures are used in the evaluation, and the data for the Turkish sample between February 2003 and December 2022 are analysed. The data are analysed by subjecting them to Traditional Fourier and Fractional Frequency Fourier tests. The methods used in the study minimise the margin of error as they include sine and cosine values as well as structural breaks in the analysis and are considered to be one of the most up-to-date analysis methods. According to the study’s findings, the increase in inflation rates in Türkiye does not show a permanent feature after appropriate policy adjustments.

Dataset Augmentation and Fractional Frequency Offset Compensation Based Radio Frequency Fingerprint Identification in Drone Communications

Dataset Augmentation and Fractional Frequency Offset Compensation Based Radio Frequency Fingerprint Identification in Drone Communications

Multi-qubit gates and Schrödinger cat states in an optical clock.

Many-particle entanglement is a key resource for achieving the fundamental precision limits of a quantum sensor1. Optical atomic clocks2, the current state of the art in frequency precision, are a rapidly emerging area of focus for entanglement-enhanced metrology3-6. Augmenting tweezer-based clocks featuring microscopic control and detection7-10 with the high-fidelity entangling gates developed for atom-array information processing11,12 offers a promising route towards making use of highly entangled quantum states for improved optical clocks. Here we develop and use a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger-Horne-Zeilinger (GHZ) type with up to nine optical clock qubits in a programmable atom array. In an atom-laser comparison at sufficiently short dark times, we demonstrate a fractional frequency instability below the standard quantum limit (SQL) using GHZ states of up to four qubits. However, because of their reduced dynamic range, GHZ states of a single size fail to improve the achievable clock precision at the optimal dark time compared with unentangled atoms13. Towards overcoming this hurdle, we simultaneously prepare a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval14-17. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision.

The Relationship Between Sectoral Employment and Real Sector Economic Confidence: Fourier Causation Analysis

Purpose –In order to ensure economic growth in the short term and economic development in the long term, it is important to evaluate the events occurring in the political and economic order correctly and to meet the expectations. This study was created to evaluate the effectiveness of economic confidence on the relevant sectors on a sectoral basisDesign/Methodology/Approach –In this study, the relationship between the real sector economic confidence index and employment rates in industry, construction and services sectors will be analyzed. Turkey is selected as the sample and the data range subject to the analysis is determined as 2009:01-2023:08. In the study, the Fourier analysis method, which is among the new generation analysis methods, was applied, and Fractional Frequency Fourier Augmented Dickey Fuller Unit Root Test and Fourier Toda-Yamamoto Causality Test were applied.Findings –As a result of the application, a one-way causality relationship from the real sector economic confidence index to building and industry sector employment was determined. A recommendation should be made regarding the necessity of making political arrangements that will maintain the stability level of employment in the relevant sector.Discussion –In line with the data obtained in this study, the fact that real economic confidence has an effect on employment in the construction and industrial sectors, in addition to the fact that sectoral employment has no effect on the real economic confidence index, can be linked to the fact that sectoral leaders pursue a policy of contraction or expansion within the framework of expectations

Design and Analysis of a Fractional Frequency Synthesizer With <90-fs Jitter and <–103-dBc Spurious Tones Using Digital Spur Cancellation

Design and Analysis of a Fractional Frequency Synthesizer With <90-fs Jitter and <–103-dBc Spurious Tones Using Digital Spur Cancellation

Cryogenic sapphire optical reference cavity with crystalline coatings at 1 × 10-16 fractional frequency instability.

The frequency stability of a laser locked to an optical reference cavity is fundamentally limited by thermal noise in the cavity length. These fluctuations are linked to material dissipation, which depends on both the temperature of the optical components and the material properties. Here, the design and experimental characterization of a sapphire optical cavity operated at 10K with crystalline coatings at 1069nm is presented. Theoretical estimates of the thermo-mechanical noise indicate a thermal noise floor below 4.5 × 10-18. Major technical noise contributions including vibrations, temperature fluctuations, and residual amplitude modulation are characterized in detail. The short-term performance is measured via a three-cornered hat analysis with two other cavity-stabilized lasers, yielding a noise floor of 1 × 10-16. The long-term performance is measured against an optical lattice clock, indicating cavity stability at the level of 2 × 10-15 for averaging times up to 10 000s.

Validity of Unemployment Hysteresis in European Countries and Türkiye with Fourier Functions

Unemployment hysteresis means that rising unemployment does not return to the average over time. This situation underlines that unemployment in countries is not temporary but permanent. In the case of unemployment hysteresis, economists argue for intervention in the economy. The existence of unemployment hysteresis is therefore important for the applicability of economic policy. This issue, which is very important for economists, has been analyzed in the literature using different methods. In this study, we use the analyses obtained by adding the recently popular Fourier models to unit root tests. The Flexible Fourier ADF (FF-ADF) test developed by Enders and Lee (2012) and the Fractional Frequency Flexible Fourier ADF (FFFF-ADF) test developed by Omay (2015) are used to investigate the existence of unemployment hysteresis in Türkiye and EU countries. As a result, it is found that the Fourier properties are statistically significant for both Türkiye and the EU and that the series have nonlinear properties. As a result of the tests applied, there is evidence that unemployment hysteresis does not valid for Türkiye and the EU.

Relationship Between Financial Development and Carbon Emissions: Empirical Evidence from Türkiye with Fractional Frequency Fourier Approaches

Abstract This study empirically analyzes the relationship between carbon emissions, one of the most important indicators of environmental pollution, and financial development. Using data from Türkiye for the period 1995-2019, the fractional frequency Fourier ADL cointegration method -previously unused in similar studies- is employed for the analysis. The results, which also account for economic growth, demonstrate a cointegration relationship between the variables. Additionally, the FMOLS method is utilized for model estimation, concluding that financial development and growth lead to increased carbon emissions. The study suggests that loans provided to the financial sector should be directed towards technological investments that reduce carbon emissions

Do the Political Uncertainty and Geopolitical Risk Indexes in the G-7 Countries Relate to Stock Prices? Fourier Causality Test Evidence

This study aims to examine the reciprocal effects of the Economic Policy Uncertainty (EPU) and the Geopolitical Risks (GPR) on the stock markets (SP) of the G-7 countries. The findings of the study will allow us to answer the following questions: Do risk and uncertainty conditions in other G-7 countries affect their stock markets as much as those in the country itself? Which affects G-7 stock markets more, EPU or GPR? In addition to previous research in the field, this study conducts a comparative analysis of the effects of the EPU and GPR on the SP of G-7 countries. Therefore, we used the linear VAR Granger, Fourier and Fourier Fractional Frequency Granger Causality tests. We found that the EPU indices of the United States, United Kingdom, and Germany had the greatest impact on the stock markets of their respective countries and other G-7 countries, and the conclusion that G-7 stock markets were influenced by economic uncertainties in other member countries was added to the literature. It has also been found that the G-7 stock markets have a broad influence on the EPU index.

Numerical analysis of fractional nonlinear vibrations of a restrained cantilever beam with an intermediate lumped mass

This paper focuses on the numerical investigation of the fractional nonlinear oscillator for a restrained cantilever beam with an intermediate lumped mass. A numerical approach based upon the fractional complex transformation and the global residue harmonic balance method (FCT-GRHBM) is suggested for approximately solving this fractional oscillation system of fifth-order nonlinearity. The approximated fractional periodic solutions and frequencies are provided by FCT-GRHBM, which are not touched in the existing literature. Numerical results and sensitive analysis with respect to different parameters are shown to confirm its efficiency.

W-band photonic-aided mm-wave ISAC system enabled by a shared OFDM signal waveform and a two-stage carrier frequency recovery algorithm.

Integrated sensing and communication (ISAC) systems will play a potential role in the upcoming six-generation (6G) networks. The reason is that ISAC systems can effectively solve the spectrum resource shortage problem and decrease the cost of deploying hardware equipment for simultaneously realizing communication and sensing. In this Letter, we successfully realize a W-band photonic-aided millimeter-wave (mm-wave) ISAC system enabled by a shared orthogonal-frequency-division-multiplexing (OFDM) signal waveform and two-stage carrier frequency recovery (CFR) algorithm. The digital-signal-processing (DSP)-based two-stage CFR algorithm includes the first-stage fractional frequency offset (FFO) estimation and compensation as well as the second-stage integer frequency offset (IFO) estimation and compensation. We experimentally analyze and verify that, with the introduction of the two-stage CFR algorithm, the system robustness to carrier frequency offset can be significantly enhanced. We also experimentally demonstrate, based on the ISAC system and our receiver DSP, a net data rate of up to 47.54 Gbit/s with a total signal bandwidth of 16 GHz over a 5.2 m wireless link at 94.5 GHz. Moreover, the sensing results indicate that the ISAC system can realize the detection of one target 2 m away from the transmitter with a ranging resolution of 0.98 cm and a ranging error of 4 mm. The system is anticipated to facilitate diverse potential applications in future 6G networks.

Correction: Wang et al. Optical Frequency Transfer on the Order of 10−19 Fractional Frequency Instability over a 64 m Free-Space Link. Photonics 2024, 11, 587

In the original publication [...]