Exploration of instantaneous frequency for local control assessment in real-time hybrid simulation

Local control parameters such as instantaneous delay and instantaneous amplitude play an essential role in evaluating the performance and maintaining the stability of real-time hybrid simulation(RTHS).However,existing methods have limitations in obtaining this local assessment in either the time domain or frequency domain.In this study,the instantaneous frequency is introduced to determine local control parameters for actuator tracking assessment in a real-time hybrid simulation.Instantaneous properties,including amplitude,delay,frequency and phase,are then calculated based on analytic signals translated from actuator tracking signals through the Hilbert transform.Potential issues are discussed and solutions are proposed for calculation of local control parameters.Numerical simulations are first conducted for sinusoidal and chirp signals with time varying amplitude error and delay to demonstrate the potential of the proposed method.Laboratory tests also are conducted for a predefined random signal as well as the RTHS of a single degree of freedom structure with a self-centering viscous damper to experimentally verify the effectiveness of the proposed use of the instantaneous frequency.Results from the ensuing analysis clearly demonstrate that the instantaneous frequency provides great potential for local control assessment,and the proposed method enables local tracking parameters with good accuracy.

Improving the utility of locally differentially private protocols for longitudinal and multidimensional frequency estimates

This paper investigates the problem of collecting multidimensional data throughout time(i.e.,longitudinal studies)for the fundamental task of frequency estimation under Local Differential Privacy(LDP)guarantees.Contrary to frequency estimation of a single attribute,the multidimensional aspect demands particular attention to the privacy budget.Besides,when collecting user statistics longitudinally,privacy progressively degrades.Indeed,the“multiple”settings in combination(i.e.,many attributes and several collections throughout time)impose several challenges,for which this paper proposes the first solution for frequency estimates under LDP.To tackle these issues,we extend the analysis of three state-of-the-art LDP protocols(Generalized Randomized Response–GRR,Optimized Unary Encoding–OUE,and Symmetric Unary Encoding–SUE)for both longitudinal and multidimensional data collections.While the known literature uses OUE and SUE for two rounds of sanitization(a.k.a.memoization),i.e.,L-OUE and L-SUE,respectively,we analytically and experimentally show that starting with OUE and then with SUE provides higher data utility(i.e.,L-OSUE).Also,for attributes with small domain sizes,we propose Longitudinal GRR(L-GRR),which provides higher utility than the other protocols based on unary encoding.Last,we also propose a new solution named Adaptive LDP for LOngitudinal and Multidimensional FREquency Estimates(ALLOMFREE),which randomly samples a single attribute to be sent with the whole privacy budget and adaptively selects the optimal protocol,i.e.,either L-GRR or L-OSUE.As shown in the results,ALLOMFREE consistently and considerably outperforms the state-of-the-art L-SUE and L-OUE protocols in the quality of the frequency estimates.

High Sensitivity Digital Instantaneous Frequency Measurement Receiver for Precise Frequency Analysis

There are numerous applications, such as Radar, that leverage wideband technology. However, the presence of noise introduces certain limitations and challenges. It is crucial to harness wideband technology for applications demanding the rapid and precise transmission of diverse information from one point to another within a short timeframe. The ability to report a signal without tuning within the input bandwidth stands out as one of the advantages of employing a digital wideband receiver. As indicated, a digital wideband receiver plays a pivotal role in achieving high precision and accuracy. The primary distinction between Analog and Digital Instantaneous Frequency Measurement lies in the fact that analog Instantaneous Frequency Measurement (IFM) receivers have traditionally covered extensive input bandwidths, reporting one accurate frequency per short pulse. In the contemporary landscape, digital IFM systems utilize high-sampling-rate Analog-to-Digital Converters (ADC) along with Hilbert transforms to generate two output channels featuring a 90-degree phase shift. This paper explores the improvement of sensitivity in current digital IFM receivers. The optimization efforts target the Hilbert transform and autocorrelations architectures, aiming to refine the system’s ability to report fine frequencies within a noisy wide bandwidth environment, thereby elevating its overall sensitivity.

High-Precision Doppler Frequency Estimation Based Positioning Using OTFS Modulations by Red and Blue Frequency Shift Discriminator

Orthogonal Time Frequency and Space(OTFS) modulation is expected to provide high-speed and ultra-reliable communications for emerging mobile applications, including low-orbit satellite communications. Using the Doppler frequency for positioning is a promising research direction on communication and navigation integration. To tackle the high Doppler frequency and low signal-to-noise ratio(SNR) in satellite communication, this paper proposes a Red and Blue Frequency Shift Discriminator(RBFSD) based on the pseudo-noise(PN) sequence.The paper derives that the cross-correlation function on the Doppler domain exhibits the characteristic of a Sinc function. Therefore, it applies modulation onto the Delay-Doppler domain using PN sequence and adjusts Doppler frequency estimation by red-shifting or blue-shifting. Simulation results show that the performance of Doppler frequency estimation is close to the Cramér-Rao Lower Bound when the SNR is greater than -15dB. The proposed algorithm is about 1/D times less complex than the existing PN pilot sequence algorithm, where D is the resolution of the fractional Doppler.

Enhanced Wideband Frequency Estimation via FFT: Leveraging Polynomial Interpolation and Array Indexing

Accurate frequency estimation in a wideband digital receiver using the FFT algorithm encounters challenges, such as spectral leakage resulting from the FFT’s assumption of signal periodicity. High-resolution FFTs pose computational demands, and estimating non-integer multiples of frequency resolution proves exceptionally challenging. This paper introduces two novel methods for enhanced frequency precision: polynomial interpolation and array indexing, comparing their results with super-resolution and scalloping loss. Simulation results demonstrate the effectiveness of the proposed methods in contemporary radar systems, with array indexing providing the best frequency estimation despite utilizing maximum hardware resources. The paper demonstrates a trade-off between accurate frequency estimation and hardware resources when comparing polynomial interpolation and array indexing.

DEVELOPMENT OF VIRTUAL INSTRUMENT IN CHARACTERISTIC ANALYSIS OF ROTATING MACHINERY BASED ON INSTANTANEOUS FREQUENCY ESTIMATION

Based on the recently quick-developing time-frequency analysis (TFA)technique and virtual instrument (VI) technique, a virtual instrument in characteristic analysis ofrotating machinery is researched and developed successfully. By utilizing instantaneous frequencyestimation (IFE) theoretics of TFA technique, and based on IFE of peak searching on thetime-frequency spectrum, order analysis (OA) functions is put forward and implemented, such as orderspectrum, order spectrum matrix, order tracking, order tracking filtering, and order componentextraction, etc. Unlike the home and abroad existing popular characteristic analyzers, which needkey phasing devices such as shaft encoder, phase-locked loop (PLL), phase-locked multiple frequency,tachometer, etc, to implement constant angle sampling directly or indirectly, whereas thisinstrument only uses the vibration signal of rotating machinery to carry out OA. This instrumentmakes up the shortage of these traditional instruments in analyzing the non-stationary signal ofrun-up and run-down process of rotating machinery. Therefore, it is a great breakthrough for theexisting order analyzers.

Rolling element bearing instantaneous rotational frequency estimation based on EMD soft-thresholding denoising and instantaneous fault characteristic frequency

The accurate estimation of the rolling element bearing instantaneous rotational frequency(IRF) is the key capability of the order tracking method based on time-frequency analysis. The rolling element bearing IRF can be accurately estimated according to the instantaneous fault characteristic frequency(IFCF). However, in an environment with a low signal-to-noise ratio(SNR), e.g., an incipient fault or function at a low speed, the signal contains strong background noise that seriously affects the effectiveness of the aforementioned method. An algorithm of signal preprocessing based on empirical mode decomposition(EMD) and wavelet shrinkage was proposed in this work. Compared with EMD denoising by the cross-correlation coefficient and kurtosis(CCK) criterion, the method of EMD soft-thresholding(ST) denoising can ensure the integrity of the signal, improve the SNR, and highlight fault features. The effectiveness of the algorithm for rolling element bearing IRF estimation by EMD ST denoising and the IFCF was validated by both simulated and experimental bearing vibration signals at a low SNR.

IMPROVED METHOD FOR HILBERT INSTANTANEOUS FREQUENCY ESTIMATION

In the mechanical fault detection and diagnosis field, it is more and more important to analyze the instantaneous frequency （IF） character of complex vibration signal. The improved IF estimation method is put forward aiming at the shortage of traditional Hilbert transform. It is based on Hilbert transform in wavelet domain. With the help of relationship between the real part and the imaginary part obtained from the complex coefficient of continuous wavelet transform or the analyti- cal signal reconstructed in wavelet packet decomposition, the instantaneous phase function of the subcomponent is extracted. In order to improve the precise of IF estimated out, some means such as Linear regression, adaptive filtering, resampling are applied into the instantaneous phase obtained, then, the central differencing operator is used to get desired IF. Simulation results with synthetic and gearbox fault signals are included to illustrate the proposed method.

Instantaneous frequency estimation of multi-component Chirp signals in noisy environments

A classical time-varying signal, the multi-component Chirp signal has been widely used and the ability to estimate its instantaneous frequency （IF） is very useful. But in noisy environments, it is hard to estimate the 1F of a multi-component Chirp signal accurately. Wigner distribution maxima （WDM） are usually utilized for this estimation. But in practice, estimation bias increases when some points deviate from the true IF in high noise environments. This paper presents a new method of multi-component Chirp signal 1F estimation named Wigner Viterbi fit （WVF）, based on Wigner-Ville distribution （WVD） and the Viterbi algorithm. First, we transform the WVD of the Chirp signal into digital image, and apply the Viterbi algorithm to separate the components and estimate their IF. At last, we establish a linear model to fit the estimation results. Theoretical analysis and simulation results prove that this new method has high precision and better performance than WDM in high noise environments, and better suppression of interference and the edge effect. Compared with WDM, WVF can reduce the mean square error （MSE） by 50% when the signal to noise ration （SNR） is in the range of-15dB to -11dB. WVF is an effective and promising 1F estimation method.

Signal Separation and Instantaneous Frequency Estimation Based on Multi-scale Chirplet Sparse Signal Decomposition

An approach based on multi-scale ehirplet sparse signal decomposition is proposed to separate the malti-component polynomial phase signals, and estimate their instantaneous frequencies. In this paper, we have generated a family of multi-scale chirplet functions which provide good local correlations of chirps over shorter time interval. At every decomposition stage, we build the so-called family of chirplets and our idea is to use a structured algorithm which exploits information in the family to chain chirplets together adaptively as to form the polyncmial phase signal component whose correlation with the current residue signal is largest. Simultaueously, the polynomial instantaneous frequency is estimated by connecting the linear frequency of the chirplet functions adopted in the current separation. Simulation experiment demonstrated that this method can separate the camponents of the multi-component polynamial phase signals effectively even in the low signal-to-noise ratio condition, and estimate its instantaneous frequency accurately.

Intelligent recognition and information extraction of radar complex jamming based on time-frequency features

In modern war,radar countermeasure is becoming increasingly fierce,and the enemy jamming time and pattern are changing more randomly.It is challenging for the radar to efficiently identify jamming and obtain precise parameter information,particularly in low signal-to-noise ratio(SNR)situations.In this paper,an approach to intelligent recognition and complex jamming parameter estimate based on joint time-frequency distribution features is proposed to address this challenging issue.Firstly,a joint algorithm based on YOLOv5 convolutional neural networks(CNNs)is proposed,which is used to achieve the jamming signal classification and preliminary parameter estimation.Furthermore,an accurate jamming key parameters estimation algorithm is constructed by comprehensively utilizing chi-square statistical test,feature region search,position regression,spectrum interpolation,etc.,which realizes the accurate estimation of jamming carrier frequency,relative delay,Doppler frequency shift,and other parameters.Finally,the approach has improved performance for complex jamming recognition and parameter estimation under low SNR,and the recognition rate can reach 98%under−15 dB SNR,according to simulation and real data verification results.

Frame Length Dependency for Fundamental Frequency Extraction in Noisy Speech

The fundamental frequency plays a significant part in understanding and perceiving the pitch of a sound. The pitch is a fundamental attribute employed in numerous speech-related works. For fundamental frequency extraction, several algorithms have been developed which one to use relies on the signal’s characteristics and the surrounding noise. Thus, the algorithm’s noise resistance becomes more critical than ever for precise fundamental frequency estimation. Nonetheless, numerous state-of-the-art algorithms face struggles in achieving satisfying outcomes when confronted with speech recordings that are noisy with low signal-to-noise ratio (SNR) values. Also, most of the recent techniques utilize different frame lengths for pitch extraction. From this point of view, This research considers different frame lengths on male and female speech signals for fundamental frequency extraction. Also, analyze the frame length dependency on the speech signal analytically to understand which frame length is more suitable and effective for male and female speech signals specifically. For the validation of our idea, we have utilized the conventional autocorrelation function (ACF), and state-of-the-art method BaNa. This study puts out a potent idea that will work better for speech processing applications in noisy speech. From experimental results, the proposed idea represents which frame length is more appropriate for male and female speech signals in noisy environments.

Parameter estimation method for a linear frequency modulation signal with a Duffing oscillator based on frequency periodicity

In view of the complexity of existing linear frequency modulation(LFM)signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio(SNR),a parameter estimation method for LFM signals with a Duffing oscillator based on frequency periodicity is proposed in this paper.This method utilizes the characteristic that the output signal of the Duffing oscillator excited by the LFM signal changes periodically with frequency,and the modulation period of the LFM signal is estimated by autocorrelation processing of the output signal of the Duffing oscillator.On this basis,the corresponding relationship between the reference frequency of the frequencyaligned Duffing oscillator and the frequency range of the LFM signal is analyzed by the periodic power spectrum method,and the frequency information of the LFM signal is determined.Simulation results show that this method can achieve high-accuracy parameter estimation for LFM signals at an SNR of-25 dB.

Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.

A High Spectral Efficient Frequency-Domain Channel-Estimation Method for the Polarization-Division-Multiplexed CO-OFDM-OQAM System

Contrary to the other multi-carrier modulation systems, the coherent optical orthogonal frequency division multiplexing communication system with an offset quadrature amplitude modulation (CO-OFDM-OQAM) possesses inherent imaginary interference (IMI). This has an important impact on the channel estimation process. Currently, a variety of frequency-domain channel estimation methods have been proposed. However, there are various problems that still exist. For instance, in order to reduce the influence of IMI, it is necessary to insert more guard intervals between the training sequence and the payload, leading to the occupation of excessive spectrum resources. In order to address this problem, this work designs a high spectral efficient frequency-domain channel estimation method for the polarization-division-multiplexing CO-OFDM-OQAM systems. First, the working principle of the proposed method is described in detail. Then, its spectral efficiency, power peak-to-average ratio, and channel estimation performance are studied based on simulations. The simulation results show that the proposed method improves the spectral efficiency without worsening the power peak-to-average ratio. The channel estimation capability of this method is verified in three scenarios of long-distance transmissions, including back-to-back, 100 km, and 200 km transmissions. .

Instantaneous frequency and wave mode identification in a magnetosheath using few spatial points

Observational data such as those obtained from the magnetosheath in the downstream of Earth＇s bow shock have waveforms that differ from those of sinusoidal signals. In practice, they are not even aggregates of sinusoidal signals. Therefore, the frequency decomposition for the data requires technique that will account for the time-varying features of the data that will lead to deduction of physical meaning of the observations. The combination of empirical mode decompo- sition （EMD） and Hilbert transform has been used for extracting the various contributing oscillatory modes （EMDs） and the instantaneous frequency determination （Hilbert transform） of every physically meaningful mode called intrinsic mode func- tion （IMF）. The resulting instantaneous frequencies are used to determine instantaneous wave vectors. The combination of the instantaneous frequencies and wave vectors is useful in the identification of wave modes based on the characteristics of the waves. The results show that EMD-Hilbert can be more reliable than simple Hilbert transform alone.

Instantaneous frequency measurement using two parallel I/Q modulators based on optical power monitoring

A scheme for instantaneous frequency measurement(IFM)using two parallel I/Q modulators based on optical power monitoring is proposed.The amplitude comparison function(ACF)can be constructed to establish the relationship between the frequency of radio frequency(RF)signal and the power ratio of two optical signals output by two I/Q modulators.The frequency of RF signal can be derived by measuring the optical power of the optical signals output by two I/Q modulators.The measurement range and measurement error can be adjusted by controlling the delay amount of the electrical delay line.The feasibility of the scheme is verified,and the corresponding measurement range and measurement error of the system under different delay amounts of the electrical delay line are given.Compared with previous IFM schemes,the structure of this scheme is simple.Polarization devices,a photodetector and an electrical power meter are not used,which reduces the impact of the environmental disturbance on the system and the cost of the system.In simulation,the measurement range can reach 0 GHz-24.5 GHz by adjusting the delay amount of the electrical delay lineτ=20 ps.The measurement error of the scheme is better at low frequency,and the measurement error of low frequency 0 GHz-9.6 GHz can reach-0.1 GHz to+0.05 GHz.

A Cell Condition-Sensitive Frequency Segmentation Method Based on the Sub-Band Instantaneous Energy Spectrum of Aluminum Electrolysis Cell Voltage

Cell voltage is a widely used signal that can be measured online from an industrial aluminum electrolysis cell.A variety of parameters for the analysis and control of industrial cells are calculated using the cell voltage.In this paper,the frequency segmentation of cell voltage is used as the basis for designing filters to obtain these parameters.Based on the qualitative analysis of the cell voltage,the sub-band instantaneous energy spectrum(SIEP)is first proposed,which is then used to quantitatively represent the characteristics of the designated frequency bands of the cell voltage under various cell conditions.Ultimately,a cell condition-sensitive frequency segmentation method is given.The proposed frequency segmentation method divides the effective frequency band into the[0,0.001]Hz band of lowfrequency signals and the[0.001,0.050]Hz band of low-frequency noise,and subdivides the lowfrequency noise into the[0.001,0.010]Hz band of metal pad abnormal rolling and the[0.01,0.05]Hz band of sub-low-frequency noise.Compared with the instantaneous energy spectrum based on empirical mode decomposition,the SIEP more finely represents the law of energy change with time in any designated frequency band within the effective frequency band of the cell voltage.The proposed frequency segmentation method is more sensitive to cell condition changes and can obtain more elaborate details of online cell condition information,thus providing a more reliable and accurate online basis for cell condition monitoring and control decisions.

Nonparametric Spectral Estimation Technique to Estimate Dominant Frequency for Atrial Fibrillation Detection

Atrial fibrillation (Afib) is related with heart failure, stroke, and high mortality rates. In frequency domain analysis, pre-requisite for Afib detection has been the estimation of reliable dominant frequency (DF) of atrial signals via different spectral estimation techniques. DF further characterizes Afib, and helps in its treatment. This paper aims at finding the most appropriate nonparametric FFT-based spectral estimation technique to estimate reliable DF for Afib detection. In this work, real-time intra-atrial electrograms have been acquired and pre-processed for frequency analysis. DF is estimated via Bartlett using Hanning window, and Welch methods. Regularity index (RI), a parameter to ensure reliability of DF, is calculated using Simpson 3/8 and Trapezoidal rules. The best method is declared based upon high accuracy of Afib detection using reliable DF. On comparison, Welch method is found to be more appropriate to estimate reliable DF for Afib detection with 98% accuracy.

A NEW ESPRIT METHOD FOR BLIND ESTIMATES OF DOA-DOPPLER FREQUENCY WITH UNKNOWN ARRAY MANIFOLD

A novel rotational invariance technique for blind estimates of direction of arrival (I)OA) and Doppler frequency with unknown array manifold due to array sensor uncertainties is proposed, taking Doppler frequency difference between a successive pulses as rotational parameter. The effectiveness of the new method is confirmed by computer simulation. Compared with the existing 2-D DOA-frequeucy estimate techniques, the computation load of the proposed method can be saved greatly.