Accurate Frequency Estimation Research Articles

An Efficient Algorithm to Retrieve Multiple Fundamental Frequencies of Harmonic Interference in Surface-NMR Measurements

Summary The successful recovery of hydrogeophysical parameters through surface-NMR measurements depends on the quality of the signal, which can be significantly degraded by harmonics from multiple noise sources with different fundamental frequencies in urban areas. Accurate estimation of the fundamental frequencies of harmonics is the main step in harmonic noise cancellation-based methods. The existing 1D and 2D model-based approaches involve a computationally expensive process that sets limits for processing of large surface-NMR data sets. In addition, the classical Nyman, Gaiser, and Saucier estimation (NGSE) algorithm, despite its fast implementation, may not accurately recover harmonic components when there is no prior knowledge of the expected value of the frequency offset between the true fundamental frequencies and their nominal values. This lack of knowledge can make it difficult to accurately estimate the maximum number of harmonics and, consequently, result in an incorrect recovery of the fundamental frequency. To surmount these limitations, we propose an enhanced version of the NGSE approach based on an efficient maximum number of harmonics search approach to process surface-NMR signals corrupted by powerline harmonics with both single and multiple frequency content. We verify the efficiency of our algorithm on a synthetic dataset embedded in simulated powerline harmonic signals, and real electromagnetic noise recordings, as well as a real surface-NMR data set. Our numerical experiments confirm that the proposed algorithm can retrieve the multiple fundamental frequencies simultaneously with a significant speedup ranging from 4 to 87 times, depending on whether the signal has single, dual, or triple frequency content, in the overall computation time compared to the model-based methods.

Radial vibration measurement of rotating shaft using constant density fringe pattern and line scan camera

The radial vibration signals of the rotor can provide abundant information about the health condition of the machine. In this paper, a simple vision-based measurement system is proposed to simultaneously measure two-dimensional displacements in radial directions for the rotating shaft, where the system consists of a constant density fringe pattern (CDFP), a line scan camera (LSC), and a lens. The CDFP should be installed around the surface of the rotating shaft to make the density of the fringe constant along the shaft axis, while the shaft axis is vertical to the optical axis of the LSC but not parallel to the line-array sensor of the LSC. Therefore, the density of the fringe imaged on the LSC is not constant because of the modulation of the circular surface of the shaft, and the distribution of the fringe density on the LSC is a U-shaped curve. Thus, the shaft centreline orbit can be tracked by the lowest point of the density distribution curve (DDC) of the fringe. Then, an efficient and accurate parameterized instantaneous frequency estimation method is employed to estimate the DDC of the fringe, because the variable density fringe can be regarded as an amplitude-modulated and frequency-modulated nonstationary signal whose instantaneous frequency function is equivalent to the DDC. Experimental results verify the feasibility and effectiveness of the proposed method by comparing it to the eddy current sensors.

Assisting the analysis of insertions and deletions using regional allele frequencies.

Accurate estimation of population allele frequency (AF) is crucial for gene discovery and genetic diagnostics. However, determining AF for frameshift-inducing small insertions and deletions (indels) faces challenges due to discrepancies in mapping and variant calling methods. Here, we propose an innovative approach to assess indel AF. We developed CRAFTS-indels (Calculating Regional Allele Frequency Targeting Small indels), an algorithm that combines AF of distinct indels within a given region and provides "regional AF" (rAF). We tested and validated CRAFTS-indels using three independent datasets: gnomAD v2 (n=125,748 samples), an internal dataset (IGM; n=39,367), and the UK BioBank (UKBB; n=469,835). By comparing rAF against standard AF, we identified rare indels with rAF exceeding standard AF (sAF≤10-4 and rAF>10-4) as "rAF-hi" indels. Notably, a high percentage of rare indels were "rAF-hi", with a higher proportion in gnomAD v2 (11-20%) and IGM (11-22%) compared to the UKBB (5-9% depending on the CRAFTS-indels' parameters). Analysis of the overlap of regions based on their rAF with low complexity regions and with ClinVar classification supported the pertinence of rAF. Using the internal dataset, we illustrated the utility of CRAFTS-indel in the analysis of de novo variants and the potential negative impact of rAF-hi indels in gene discovery. In summary, annotation of indels with cohort specific rAF can be used to handle some of the limitations of current annotation pipelines and facilitate detection of novel gene disease associations. CRAFTS-indels offers a user-friendly approach to providing rAF annotation. It can be integrated into public databases such as gnomAD, UKBB and used by ClinVar to revise indel classifications.

HeavySeparation: A Generic framework for stream processing faster and more accurate

Sketch as a probability data structure has been widely used in high volume, fast data streams. At the cost of a tiny accuracy in frequency estimation, it achieves a high speed with small memory usage. However, skewed data streams pose a significant challenge for existing sketches in terms of accuracy and speed using limited memory. To address this issue, we proposed a framework, called HeavySeparation, to enhance existing sketches by filtering elephant flow efficiently and accurately. We adopt a power-weakening increment strategy to allow sufficient competition in the early stages of identifying elephant flows and amplifying relative advantage when the frequency of candidate flow is large. To verify the effectiveness and efficiency of our framework, we apply the framework to two typical sketches and two common stream processing tasks. Results show that HeavySeparation framework reduces the error by around 1–2 orders of magnitude on average compared to the state-of-the-art in frequency estimation.

Optimizing Bangkaew dog breed identification using DNA technology.

The Bangkaew dog is an indigenous dog breed in the Phitsanulok province of Thailand. This breed is recognized by the Fédération Cynologique Internationale (FCI), a global canine organization. The unique traits of the Bangkaew breed lead to purebred selection for breeding, while only their traits and pedigree from parental history are recorded. Determination of the risk of inbreeding depression and the origin of unknown DNA profiles is essential due to the challenges in predicting puppy characteristics, which are crucial for breed management and conservation. This study aimed to emphasize that current allelic frequency data for the Bangkaew dog breed must be considered for precise individual identification. Approximately 82 Bangkaew dogs from various Thai localities were studied using 15 microsatellite markers for genotypic monitoring and individual identification. Maternal genetic inheritance was assessed via mtDNA D-loop analysis. The results revealed high genetic diversity in the Bangkaew breed, indicating low potential for inbreeding. We also found that using a 15 loci microsatellite panel was effective for the identification of Bangkaew dogs. The optimized 10 loci microsatellite genotyping panel developed in this study presents improved identification testing efficiency, promoting both time- and cost-effectiveness. Analysis of microsatellite DNA markers in Bangkaew dogs using an optimized panel of 10 loci selected from 15 loci effectively facilitated individual identification. This approach not only enhances time and cost efficiency, but also provides accurate allelic frequency estimates, which are crucial for the realistic evaluation of DNA evidence.

A novel design method for a family of single-phase frequency estimators based on discrete oscillator for micro-grid application

The family of frequency estimators based on discrete oscillator is believed to be the simplest one for single-phase grid voltage. In order to make this family of frequency estimators more feasible in micro-grid, a novel design is proposed in this paper. The novelty includes a clear input–output relationship for the family of frequency estimators based on the discrete oscillator, an optimized design of the discrete oscillator model (DOM), and an enhanced pre-filter. Firstly, the input–output relationship is established by the time-domain feedback analysis, and it reveals that the frequency estimators inherently possess complex-coefficient comb filtering ability. Then, an optimized DOM design is presented to enhance the frequency estimators' filtering ability near the nominal frequency. Lastly, an enhanced pre-filter is proposed to match this optimized DOM for high filtering ability in a wide frequency range. The proposed design method has no stability issues and a very low computational burden. Compared with previous methods, the proposed method demonstrates higher accuracy in frequency estimation and similar response speed in micro-grid with significant frequency fluctuation and harmonic pollution, verified by experimental results.

Improved windowed phase difference method for frequency estimation of distorted power signals

Frequency is one of the most significant indicators of power system, which needs accurate estimation to provide a reliable basis for monitoring, control, and protection. Owning to the efficiency, DFT is widely used in the frequency measurement of power systems. However, the inherent defects, that is, the spectral leakage and picket fence effect, decrease the accuracy of DFT. One of the variants, named the windowed phase difference method (WPD), addresses the problem using the phase variation of two windowed sequences in the frequency domain and achieves accurate frequency estimation. Suffering from the ignored negative component and contamination of noise, there are still undesired errors in WPD-based frequency estimation. To reduce the influence of the undesired errors, this paper first analyzes the systematic error of WPD introduced by spectrum leakage and proposes an improved WPD (IWPD) through systematic error compensation to achieve more accurate frequency estimations. Then, the windowing effect on IWPD-based frequency estimation of a noisy signal is studied by deducing the theoretical expression of frequency estimation variance. Finally, the proposed IWPD is validated by extensive computer simulations and practical experiments.

Delay-Tracking Loop for Frequency Estimation of Grid-Interfaced Inverter Under Distorted Conditions

Fast and accurate frequency estimation is difficult for grid-interfaced inverter under distorted grid conditions with off-nominal frequency. A popular solution considers the multiple second-order generalized integrator-based frequency-locked loop yet can hardly achieve a fast dynamic response under significant phase jump and voltage sag. Another solution uses an adaptive sliding window filter with an additional frequency estimator. However, it is challenging to handle numerical instability due to the adjusting marginally-stable resonator and the accumulation error. This letter proposes a delay-tracking loop to overcome these problems. This loop allows the delay length to track the frequency with an inherent harmonics rejection at off-nominal frequency. At the same time, the fast response speed is maintained, and the marginally stable resonator is avoided. Comparative experimental results validate the above claims.

The Accuracy of Frequency Estimation of Structure Vibration under Ambient Excitation: Problems, Causes, and Methods

Accurate identification of building structure frequencies forms the basis for damage detection. The structural dynamic response signal, under ambient excitation, can be transformed into a superposition of multiple single-frequency exponentially damped sinusoids combined with random white noise. However, the peak power spectrum of the response signal tends to exhibit line splitting, compromising the precision of frequency identification. This study examines the accuracy characteristics of the single-frequency free damping vibration signal (SFFDVS) and derives the Cramer–Rao lower bound for the frequency estimator. It thoroughly analyzes the factors influencing the accuracy of SFFDVS frequency identification. The study reveals that the primary cause of spectral line splitting is the random delay inherent in SFFDVS. Based on the maximum likelihood method (MLM), this research introduces the MLM algorithm for SFFDVS and provides a simulation analysis. The findings indicate that the MLM estimation algorithm for frequency parameters effectively addresses spectral line splitting and offers robust noise resistance and recognition accuracy.

Damage inference and residual capacity assessment for an E-Defense 2018 ten-story RC test structure

This paper presents an enhanced vision-based, post-earthquake performance assessment framework for RC building structures. This framework incorporates a damage inference method that can estimate the stiffness and strength reduction factors of components in stories without damage inspection based on the inter-story drift. The framework was validated by the application to the full-scale shaking table test of an E-Defense 2018 ten-story RC structure. The vision-based damage detection method effectively detected multicategory seismic damage on the component surfaces, and the damage states estimated by the vision-based method were consistent with the results estimated by the measured plastic hinge rotation. The proposed inter-story drift-based damage inference method reasonably estimated the reduction factors of components in the stories without damage photos. The numerical model updated by the reduction factors of damaged components provided accurate estimates of the fundamental vibrational frequencies after different levels of seismic shaking, and the drift-based inference method significantly improved the results compared with the trivial linear interpolation method. The residual capacity curves provided by pushover analysis of the updated model using the reduction factors as per FEMA 306 & Chiu et al. reasonably captured the hysteretic responses of the structure.

Carrier-frequency estimation for digital holograms of phase objects.

Accurate estimation of carrier fringe frequency is essential for the demodulation of off-axis digital holograms. The fringe frequency is often associated with the amplitude peak of the cross-term in the two-dimensional Fourier transform of a digital hologram. We point out that this definition of carrier frequency is not valid in general for holograms associated with phase objects. We examine the carrier-envelope representation for digital holograms from the viewpoint of Mandel's criterion [J. Opt. Soc. Am.57, 613 (1967)10.1364/JOSA.57.000613]. An appropriate definition of carrier frequency is observed to be the centroid of the power spectrum associated with the cross term. This definition is shown to apply uniformly to holograms associated with phase objects, is robust to noise, and leads to the smoothest (or least fluctuating) envelope representation for the demodulated object wave. The proposed definition is illustrated with simulated as well as experimentally recorded off-axis holograms.

Echo Frequency Estimation Technology for Passive Surface Acoustic Wave Resonant Sensors Based on a Genetic Algorithm

Passive wireless surface acoustic wave (SAW) resonant sensors are widely used in measuring pressure, temperature, and torque, typically detecting sensing parameters by measuring the echo signal frequency of SAW resonators. Therefore, the accuracy of echo signal frequency estimation directly affects the performance index of the sensor. Due to the exponential attenuation trend of the echo signal, the duration is generally approximately 10 μs, with conventional frequency domain analysis methods limited by the sampling frequency and data points. Thus, the resolution of frequency estimation is limited. Here, signal time-domain fitting combined with a genetic algorithm is used to estimate SAW echo signal frequency. To address the problem of slow estimation speed and poor timeliness caused by a conventional genetic algorithm, which needs to simultaneously estimate multiple parameters, such as signal amplitude, phase, frequency, and envelope, the Hilbert transform is proposed to remove the signal envelope and estimate its amplitude, and the fast Fourier transform subsection method is used to analyze the initial phase of the signal. The genetic algorithm is thereby optimized to realize the frequency estimation of SAW echo signals under a single parameter. The developed digital signal processing frequency detection system was monitored in real time to estimate the frequency of an SAW echo signal lasting 10 μs and found to have only 100 sampling points. The proposed method has a frequency estimation error within 3 kHz and a frequency estimation time of less than 1 s, which is eight times faster than the conventional genetic algorithm.

Multisynchrosqueezing short-time fractional Fourier transform and its application in rolling bearing instantaneous frequency estimation

Multisynchrosqueezing transform (MSST) enhances the time-frequency energy concentration by using iterative reassignment operations in time-frequency analysis (TFA). However, its effectiveness is limited for signals with rapidly changing instantaneous frequency. To address this issue, this paper presents a novel time-frequency representation (TFR) method called multisynchrosqueezing short-time fractional Fourier transform, which offers improved TF concentration for strongly frequency-modulated signals. Firstly, a high-resolution TFR of the signal is obtained by locally optimized short-time fractional Fourier transform (STFrFT). Secondly, iterative synchrosqueezing operations are introduced to further enhance the STFrFT energy concentration, with a termination strategy relying on Rényi entropy proposed to ascertain the optimal number of iterations. Finally, the ideal TFA with high energy concentration is achieved. The proposed method was validated using multi-scene simulated signals and variable-speed bearing signals. The results show that the proposed method exhibits superior time-frequency energy concentration and instantaneous frequency estimation accuracy. The estimation error of the method is consistently at least 40% lower than that of the compared short-time Fourier transform-based methods, as assessed through the evaluation criteria of maximum relative error, mean square error and symmetric mean absolute percentage error.

Adapted Weighted Linear Prediction with Attenuated Main Excitation for formant frequency estimation in high-pitched singing

This paper aims to show how to improve the accuracy of formant frequency estimation in the singing voice of a lyric soprano. Conventional methods of formant frequency estimation may not accurately capture the formant frequencies of the singing voice, particularly in the highest pitch range of a lyric soprano, where the lowest formants are biased by the pitch harmonics. To address this issue, the study proposes adapting the Weighted Linear Prediction with Attenuated Main Excitation (WLP-AME) method for formant frequency estimation. Specific methods for glottal closure instant estimation were required due to differences in glottal closure patterns between speech and singing. The study evaluates the accuracy of the proposed method by comparing its performance with the LPC method through different pitch series arranged in an ascending musical scale. The results indicated that the adapted WLP-AME method consistently outperformed the LPC method in estimating formant frequencies of vowels sung by a lyric soprano. In addition, by estimating the formant frequencies of a synthetic /i/ vowel sung by a soprano singer at the musical note E5, the study showed that the adapted WLP-AME method provided formant frequency values closer to the correct values than those estimated by the LPC method. In general, these results suggest parameter values of AME function that optimize its performance, which can have applications in fields such as singing and medicine.

Estimating the frequencies of vibration signals using a machine learning algorithm with explained predictions

Signals of short duration and containing a small number of cycles require special procedures if the precise estimation of their frequencies is intended. In this paper, we present an algorithm that allows accurate estimation of frequencies and simultaneously explains the decision regarding the prediction made. We first show why predictions regarding the frequency of signals mentioned above can contain significant errors and the prediction dependency on the analysis time. We then prove that the errors are systematic, and it is possible to train a neural network to quantify the errors and later correct the predictions. The algorithm also indicates the level of error by analyzing the signal-to-noise ratio. The algorithm was tested for numerous similar cases and proved to be reliable. At the end of the paper, we present how to use the algorithm using a signal generated with a known frequency.

Underwater spectral line enhancement and transient interference suppression based on constrained non-negative matrix factorization

Spectral line enhancement and transient interference suppression of underwater objects are critical issues for passive sonar systems. Conventional approaches for processing spectral lines have focused on either time-domain or frequency-domain methods. In this study, the constrained non-negative matrix factorization is proposed to process the underwater spectral lines in the joint time-frequency domain. Based on the sparsity of spectral lines in the frequency domain, the sparseness criterion is utilized to constrain the basis matrix that represents the frequency-mode of the signal. The correlation between sparsity and frequency estimation accuracy is examined with weight coefficients, and an effective weight coefficient interval for the sparseness term is determined to optimize the detection of the spectral line. To address the issue of abrupt changes in signal energy caused by transient interference, the temporal continuity criterion is applied to constrain the coefficient matrix representing the temporal gain mode of the signal. An analysis is conducted to determine the impact of weight coefficient on the continuity of the coefficient matrix, and the optimal weight coefficient of the temporal continuity term is established to suppress local transient strong interference. Experimental results demonstrate that the algorithm significantly enhances the capacity for the detection and extraction of spectral lines.

Intelligent Search Strategy for Doppler Frequency Based on Fuzzy Logic in DSSS Signal Acquisition

This study focuses on Doppler frequency search strategy for signal acquisition in direct sequence spread spectrum (DSSS) systems. According to DSSS signal accumulation energy vibration characteristics, the whole two-dimension search region can be divided into non-vicinity region, transition region and vicinity region. If only one search strategy is used for the whole region, it is difficult to balance the frequency search times and the frequency estimation accuracy. To solve the above problem, this study proposes an intelligent Doppler frequency search (IDFS) strategy. A fuzzy logic (FL) controller with two sets of fuzzy parameters is utilized to adjust the frequency search step size in the non-vicinity region and vicinity region, respectively. In the non-vicinity region, by jointly considering signal amplitude and code phase to design the fuzzy parameters of the FL controller, the IDFS strategy can reduce the frequency search times while reducing frequency false detection caused by abnormal change of signal energy. In the vicinity region, the fuzzy parameters are designed based on our previous work which aims to achieve higher frequency estimation accuracy. The effectiveness of the IDFS strategy is evaluated through Monte Carlo simulations. Simulation results show that the proposed intelligent search strategy can reduce the frequency search times while ensuring frequency estimation accuracy compared to other existing search strategies. Moreover, the proposed search strategy can reduce false detection in the non-vicinity region.

Compact and Accurate Phugoid Mode Approximation with Residualization

Literal approximations to the phugoid mode are systematically derived by a process of residualization with fast-slow modal decomposition. Approximations with a static residual alone and another including a dynamic residual as well are obtained. The two sets of approximations are shown to be analytically identical to each other, therefore previous attempts by some researchers to obtain "improved" literal approximations by introducing a dynamic residual are seen to be redundant. Our static residualization yields new expressions for the phugoid mode parameters which include an "inertia" term and a "phase damping" term not generally observed in previous approximations. In fact, the "phase damping" term is seen to be the second-most numerically significant damping effect after the drag and is always found to detract from phugoid damping. A third term involving the pitch damping derivative Cmq is relatively insignificant but interestingly is found in many cases to undamp the phugoid motion. Approximations are derived with and without compressibility effects in the form of the derivative CmMa to highlight the contribution of this derivative in obtaining accurate estimates of the phugoid frequency, even at low speeds. Finally, recommended literal approximations to the phugoid frequency and damping are presented which are compact and whose numerical accuracy is established for ten different combinations of airplanes / flight conditions.

Cuckoo Counter: Adaptive Structure of Counters for Accurate Frequency and Top-k Estimation

Frequency estimation and top-k flows identification are fundamental problems in network traffic measurement. Sketch, as a basic probabilistic data structure, has been extensively investigated and used in different management applications. However, few of them is suitable for both estimating frequency and finding top-k flows due to the unbalanced distribution of real-world network streams. By introducing a pre-filtering stage to isolate elephant and mice flows, the recently proposed Augmented Sketch (ASketch) significantly improves accuracy for both tasks. However, it suffers from serious performance degradation because of frequent flow exchanges. In this paper, we propose Cuckoo Counter (CC), an adaptive structure that consists of several buckets organized in a specific way. The size of the entry in each bucket is carefully designed to match the actual distribution of streams. During processing, CC hashes a flow to buckets and uses the idea of cuckoo hashing to relocate the flow if an overflow or collision happens, which contributes to fully utilizing memory. Therefore, the replacement strategy helps CC precisely record elephant flows and cover more mice flows, and also guarantees the throughput. Extensive experimental results show that CC has the highest (Freq.) accuracy, excellent (Heavy hitter / change) accuracy, highest (Top-k) precision, and competitive throughput compared to the state-of-the-art. Specifically, CC improves the throughput and accuracy by around 1 and 2 orders of magnitude respectively compared to the well-known ASketch.

PoolHelper: An R package to help in designing Pool‐Seq studies

Abstract Next‐generation sequencing of pooled samples (Pool‐seq) is an important tool in population genomics and molecular ecology. In Pool‐seq, the relative number of reads with an allele reflects the allele frequencies in the sample. However, unequal individual contributions to the pool and sequencing errors can lead to inaccurate allele frequency estimates, influencing downstream analysis. When designing Pool‐seq studies, researchers need to decide the pool size (number of individuals) and average depth of coverage (sequencing effort). An efficient sampling design should maximise the accuracy of allele frequency estimates while minimising the sequencing effort. We describe a novel tool to simulate single nucleotide polymorphism (SNP) data using coalescent theory and account for sources of uncertainty in Pool‐seq. We introduce an R package, poolHelper, enabling users to simulate Pool‐seq data under different combinations of average depth of coverage and pool size, accounting for unequal individual contributions and sequencing errors, modelled by adjustable parameters. The mean absolute error is computed by comparing the sample allele frequencies obtained based on individual genotypes with the frequency estimates obtained with Pool‐seq. poolHelper enables users to simulate multiple combinations of pooling errors, average depth of coverage, pool sizes and number of pools to assess how they influence the error of sample allele frequencies and expected heterozygosity. Using simulations under a single population model, we illustrate that increasing the depth of coverage does not necessarily lead to more accurate estimates, reinforcing that finding the best Pool‐seq study design is not straightforward. Moreover, we show that simulations can be used to identify different combinations of parameters with similarly low mean absolute errors. This can help users to define an effective sampling design by using those combinations of parameters that minimise the sequencing effort. The poolHelper package provides tools for performing simulations with different combinations of parameters (e.g. pool size, depth of coverage, unequal individual contribution) before sampling and generating data, allowing users to define sampling schemes based on simulations. This allows researchers to focus on the best sampling scheme to answer their research questions. poolHelper is comprehensively documented with examples to guide effective use.