Robust Frequency Estimation Research Articles

Algorithm of Robust Frequency Estimation in a Channel with White Gaussian Noise and Pulse Interferences

An algorithm for robust frequency estimation in a channel with additive white Gaussian noise and pulse interference is proposed. The algorithm involves iterative elimination of pulse interferences and subsequent calculation of the maximum likelihood estimate. It is demonstrated that the proposed filter-cleaner differs from the well-known Martin–Thomson filter in the functional dependence of adaptive coefficients on the estimates of parameters of distributions of the linear prediction error and the amplitude envelope of the signal. The results of mathematical modeling and numerical estimation of the threshold point of the method (0.49) are presented.

Robust Frequency Estimation in Symmetric $$\alpha $$ α -Stable Noise

The symmetric $$\alpha $$ -stable (S $$\alpha $$ S) noise is commonly encountered in a variety of applications such as wireless communications and image processing. In this work, combining the linear prediction property and $$\ell _p$$ -norm minimization, a robust frequency estimator is devised for a complex sinusoid in the presence of the S $$\alpha $$ S noise. The proposed algorithm, based on the $$\ell _p$$ -norm of the preprocessed linear prediction errors, can be regarded as the outlier-resistant version of the generalized weighted linear prediction frequency estimation approach. Computer simulations are conducted to contrast the performance of the proposed algorithm with three conventional frequency estimators. The results indicate that our method is robust to outliers and nearly optimal compared with Cramer–Rao lower bound.

Noise Robust Formant Frequency Estimation Method Based on Spectral Model of Repeated Autocorrelation of Speech

In this paper, a noise robust formant frequency estimation scheme is developed based on a spectral model matching algorithm. Considering the vocal tract as an autoregressive system, a spectral model of repeated autocorrelation function RACF of band-limited speech signal is proposed. It is shown that because of the repeated autocorrelation operation on band-limited signal, the proposed model can exhibit prominent formant characteristics. First from given noisy speech observations, an adaptive band selection criterion is developed. Next, on each resulting band-limited noisy speech signal, a repeated autocorrelation operation is carried out, which not only reduces the effect of noise but also strengthens the dominant poles corresponding to the formant frequencies. Finally, spectrum of the RACF is computed and instead of direct spectral peak picking, a model fitting scheme is introduced to find out model parameters which lead to formant estimation. The proposed algorithm has been tested on natural vowels as well as some naturally spoken sentences in the presence of different environmental noises. It is found that the proposed scheme provides better formant estimation accuracy in comparison to some of the existing methods at low levels of signal-to-noise ratio.

Using high-resolution variant frequencies to empower clinical genome interpretation

PurposeWhole-exome and whole-genome sequencing have transformed the discovery of genetic variants that cause human Mendelian disease, but discriminating pathogenic from benign variants remains a daunting challenge. Rarity is recognized as a necessary, although not sufficient, criterion for pathogenicity, but frequency cutoffs used in Mendelian analysis are often arbitrary and overly lenient. Recent very large reference datasets, such as the Exome Aggregation Consortium (ExAC), provide an unprecedented opportunity to obtain robust frequency estimates even for very rare variants.MethodsWe present a statistical framework for the frequency-based filtering of candidate disease-causing variants, accounting for disease prevalence, genetic and allelic heterogeneity, inheritance mode, penetrance, and sampling variance in reference datasets.ResultsUsing the example of cardiomyopathy, we show that our approach reduces by two-thirds the number of candidate variants under consideration in the average exome, without removing true pathogenic variants (false-positive rate<0.001).ConclusionWe outline a statistically robust framework for assessing whether a variant is “too common” to be causative for a Mendelian disorder of interest. We present precomputed allele frequency cutoffs for all variants in the ExAC dataset.

Significant reductions in human visual gamma frequency by the gaba reuptake inhibitor tiagabine revealed by robust peak frequency estimation.

The frequency of visual gamma oscillations is determined by both the neuronal excitation–inhibition balance and the time constants of GABAergic processes. The gamma peak frequency has been linked to sensory processing, cognitive function, cortical structure, and may have a genetic contribution. To disentangle the intricate relationship among these factors, accurate and reliable estimates of peak frequency are required. Here, a bootstrapping approach that provides estimates of peak frequency reliability, thereby increasing the robustness of the inferences made on this parameter was developed. The method using both simulated data and real data from two previous pharmacological MEG studies of visual gamma with alcohol and tiagabine was validated. In particular, the study by Muthukumaraswamy et al. [2013a] (Neuropsychopharmacology 38(6):1105–1112), in which GABAergic enhancement by tiagabine had previously demonstrated a null effect on visual gamma oscillations, contrasting with strong evidence from both animal models and very recent human studies was re‐evaluated. After improved peak frequency estimation and additional exclusion of unreliably measured data, it was found that the GABA reuptake inhibitor tiagabine did produce, as predicted, a marked decrease in visual gamma oscillation frequency. This result demonstrates the potential impact of objective approaches to data quality control, and provides additional translational evidence for the mechanisms of GABAergic transmission generating gamma oscillations in humans. Hum Brain Mapp 37:3882–3896, 2016. © 2016 Wiley Periodicals, Inc.

Frequency estimation of sinusoids from nonuniform samples

Sinusoid signals with multiple frequencies appear in various systems and their frequencies may carry some important features. Frequency estimation from their discrete samples is one of the fundamental problems and many frequency estimators have been proposed for uniform sampling setting. In this paper, frequency estimators based on adaptive notch filtering are proposed for nonuniform sampling setting. We observe that some dynamic systems associated with adaptive notch filters can be solved in nonuniformly sampled time steps with high accuracy. This leads us to propose a digital adaptive notch filtering method to estimate frequency of a sinusoidal signal with single frequency from its nonuniform samples. The proposed method exhibits convergent and robust frequency estimation in the presence of random sampling noises, and its variance is comparable to the Cramer–Rao lower bound in the presence of additive white noise. The above method designed for single frequency estimation could track abrupt single frequency change of an input signal, but it is not applicable directly for multiple frequency estimation. Our simulations show that the proposed estimators have robust performance for sinusoidal signals with multiple distinct frequencies, and they can be used to separate two very close frequencies of an input signal in a highly noisy sampling environment.

Robust frequency estimation in three‐phase power systems using correntropy‐based adaptive filter

In this study, the authors propose a robust adaptive algorithm for frequency estimation in three-phase power systems when the voltage readings are corrupted by random noise sources. The proposed algorithm employs the Clarke's transformed three-phase voltage (a complex signal) and augmented complex statistics to deal with both of balanced and unbalanced system conditions. To derive the algorithm, a widely linear predictive model is assumed for the Clarke's transformed signal where the frequency of system is related to the parameters of this model. To estimate the model parameters with noisy voltage reading, they utilise the notions of maximum correntropy criterion and gradient-ascent optimisation. The proposed algorithm has the computational complexity of the popular complex least-mean-squares (CLMS) algorithm, along with the robustness that is obtained by using higher-order moments beyond just second-order moments. They compare the performance of the proposed algorithm with a recently introduced augmented CLMS (ACLMS) algorithm in different conditions, including the voltage sags and presence of impulsive noises and and higher-order harmonics. Their simulation results demonstrate that the proposed algorithm provides improved frequency estimation performance compared with ACLMS especially when the measured voltages are corrupted by impulsive noise.

Instantaneous attributes analysis of seismic signals using improved HHT

As the key technique of improved Hilbert-Huang transform (HHT), ensemble empirical mode decomposition (EEMD) has a good performance of eliminating mode mixing phenomenon, which has a strong impact on the observation of seismic information. However, the intrinsic mode functions (IMF) obtained from EEMD contain noises, so that it is required to find a more robust frequency estimation method to calculate the instantaneous frequency (IF) of IMF. For this reason, the improved HHT algorithm based on the damped instantaneous frequency (DIF) is proposed to overcome the shortage of EEMD. Compared with other IF estimation methods, the DIF has strong antinoise ability and high estimation accuracy. The test results of synthetic and real seismic data show that the proposed algorithm is feasible and effective for extracting seismic instantaneous attributes.

On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data

This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., $\ell_1$ optimization and SPICE, with an infinitely dense grid. We generalize AST (atomic-norm soft thresholding) to the case of nonconsecutively sampled data (incomplete data) inspired by recent atomic norm based techniques. We present a gridless version of SPICE (gridless SPICE, or GLS), which is applicable to both complete and incomplete data without the knowledge of noise level. We further prove the equivalence between GLS and atomic norm-based techniques under different assumptions of noise. Moreover, we extend GLS to a systematic framework consisting of model order selection and robust frequency estimation, and present feasible algorithms for AST and GLS. Numerical simulations are provided to validate our theoretical analysis and demonstrate performance of our methods compared to existing ones.

A study of position independent algorithms for phone-based gait frequency detection.

Estimating gait frequency is an important component in the detection and diagnosis of various medical conditions. Smartphone-based kinematic sensors offer a window of opportunity in free-living gait frequency estimation. The main issue with smartphone-based gait frequency estimation algorithms is how to adjust for variations in orientation and location of the phone on the human body. While numerous algorithms have been implemented to account for these differences, little work has been done in comparing these algorithms. In this study, we compare various position independent algorithms to determine which are more suited to robust gait frequency estimation. Using sensor data collected from volunteers walking with a smartphone, we examine the effect of using three different time series with the magnitude, weighted sum, and closest vertical component algorithms described in the paper. We also test two different methods of extracting step frequency: time domain peak counting and spectral analysis. The results show that the choice of time series does not significantly affect the accuracy of frequency measurements. Furthermore, both time domain and spectral approaches show comparable results. However, time domain approaches are sensitive to false-positives while spectral approaches require a minimum set of repetitive measurements. Our study suggests a hybrid approach where both time-domain and spectral approaches be used together to complement each other's shortcomings.

Real-Time EMG Signal Frequency Identification

The paper deals with a method for real-time frequency analysis of the electromyogram. The method has been proposed for usage in control systems of advanced robotics for different applications. The method includes robust real-time frequency estimation with preliminary usage of bandwidth filters. The method is easy to program and requires no additional resources. The paper presents an example of experimental approbation of proposed method.

Support vector regression ‐based robust frequency estimation algorithm by instantaneous phase

There are two important factors which impact the performance of phase-based frequency estimation algorithms remarkably: the approximations of noise phase model and imperfections in phase unwrapping process. Support vector regression (SVR) exits excellent capabilities for learning unknown data and forecasting the future ones, especially under the small sample condition. Therefore, the authors introduce it to predict the variation trend of instantaneous phase and unwrap phases efficiently. Even though with that being the case, errors still exist in phase unwrapping process because of its ambiguous phase characteristic. Furthermore, a SVR-based frequency estimation algorithm is proposed and makes it immune to these error phases by means of setting the SVR's parameters properly. The results show that, compared with other phased-based algorithms, not only does the proposed one maintain a wide estimation range and quality capabilities at low frequencies, but also improves accuracy at high frequencies and decreases the impact with the initial phase. The proposed algorithm is fit for not only linear phase signal but also polynomial phase signal, under both the Gaussian and non-Gaussian condition.

Widely Linear Adaptive Frequency Estimation of Unbalanced Three-Phase Power Systems

A novel technique for online estimation of the fundamental frequency of unbalanced three-phase power systems is proposed. Based on Clarke's transformation and widely linear complex domain modeling, the proposed method makes use of the full second-order information within three-phase signals, thus promising enhanced and robust frequency estimation. The structure, mathematical formulation, and theoretical stability and statistical performance analysis of the proposed technique illustrate that, in contrast to conventional linear adaptive estimators, the proposed method is well matched to unbalanced system conditions and also provides unbiased frequency estimation. The proposed method is also less sensitive to the variations of the three-phase voltage amplitudes over time and in the presence of higher order harmonics. Simulations on both synthetic and real-world unbalanced power systems support the analysis.

Computational auditory induction as a missing-data model-fitting problem with Bregman divergence

The human auditory system has the ability, known as auditory induction, to estimate the missing parts of a continuous auditory stream briefly covered by noise and perceptually resynthesize them. In this article, we formulate this ability as a model-based spectrogram analysis and clustering problem with missing data, show how to solve it using an auxiliary function method, and explain how this method is generally related to the expectation–maximization (EM) algorithm for a certain type of divergence measures called Bregman divergences, thus enabling the use of prior distributions on the parameters. We illustrate how our method can be used to simultaneously analyze a scene and estimate missing information with two algorithms: the first, based on non-negative matrix factorization (NMF), performs analysis of polyphonic multi-instrumental musical pieces. Our method allows this algorithm to cope with gaps within the audio data, estimating the timbre of the instruments and their pitch, and reconstructing the missing parts. The second, based on a recently introduced technique for the analysis of complex acoustical scenes called harmonic-temporal clustering (HTC), enables us to perform robust fundamental frequency estimation from incomplete speech data.

A Power Electrical Signal Tracking Strategy Based on the Modulating Functions Method

The number of pieces of equipment based on static converters such as uninterrupted power systems, series or shunt compensators, and distributed generation systems is increasing in the actual power distribution systems. For correct operation in grid-connected condition, these equipment need the information about amplitude, phase angle, and frequency of the grid fundamental voltages and currents. Since noise, harmonic pollution, and frequency variations are common problems in the utility grid, then it is necessary to have systems able to extract information about the fundamental values from highly distorted signals. For these reasons, robust and accurate estimation and synchronization methods are necessary to obtain the aforementioned information also in noise environmental. This paper presents a power electrical signal tracking strategy consisting in the combined use of a simple and robust frequency estimation method based on modulating functions and an orthogonal system generator including the second-order generalized integrator. The proposed strategy has the advantages of a fast and accurate signal tracking capability and a good rejection to noise due to the low-pass filter properties of the modulating functions. The effectiveness of the proposed method is validated through comparisons with existing methods performing simulated and laboratory experiments.

Genetic algorithms based robust frequency estimation of sinusoidal signals with stationary errors

In this paper, we consider the fundamental problem of frequency estimation of multiple sinusoidal signals with stationary errors. We propose genetic algorithm and outlier-insensitive criterion function based technique for the frequency estimation problem. In the simulation studies and real life data analysis, it is observed that the proposed genetic algorithm based robust frequency estimators are able to resolve frequencies of the sinusoidal model with high degree of accuracy. Among the proposed methods, the genetic algorithm based least squares estimator, in the no-outlier scenario, provides efficient estimates, in the sense that their mean square errors attain the corresponding Cramér-Rao lower bounds. In the presence of outliers, the proposed robust methods perform quite well and seem to have a fairly high breakdown point with respect to level of outlier contamination. The proposed methods significantly do not depend on the initial guess values required for other iterative frequency estimation methods.

Robust F0 Estimation Based on Complex LPC Analysis for IRS Filtered Noisy Speech

This paper proposes a novel robust fundamental frequency (F0) estimation algorithm based on complex-valued speech analysis for an analytic speech signal. Since analytic signal provides spectra only over positive frequencies, spectra can be accurately estimated in low frequencies. Consequently, it is considered that F0 estimation using the residual signal extracted by complex-valued speech analysis can perform better for F0 estimation than that for the residual signal extracted by conventional real-valued LPC analysis. In this paper, the autocorrelation function weighted by AMDF is adopted for the F0 estimation criterion and four signals; speech signal, analytic speech signal, LPC residual and complex LPC residual, are evaluated for the F0 estimation. Speech signals used in the experiments were an IRS filtered speech corrupted by adding white Gaussian noise or Pink noise whose noise levels are 10, 5, 0, -5[dB]. The experimental results demonstrate that the proposed algorithm based on complex LPC residual can perform better than other methods in noisy environment.

Robust F0 estimation based on complex speech analysis

This paper proposes a novel robust fundamental frequency (F0) estimation algorithm based on complex‐valued speech analysis for an analytic speech signal. Since the analytic signal provides spectra only over positive frequencies, spectra can be estimated accurately at low frequencies. Consequently, it is considered that F0 estimation using the residual signal extracted by complex‐valued speech analysis can perform better for F0 estimation than that for the residual signal extracted by conventional real‐valued LPC analysis. In this paper, the autocorrelation function (AUTOC) weighted by a reciprocal of the AMDF is also adopted for the F0 estimation criterion. The proposed F0 estimation algorithm is evaluated using three criteria, AUTOC, AMDF, and the weighted AUTOC, with complex‐valued residual extracted by complex‐valued speech analysis. We also compared the proposed method with those for three signals: the speech signal, analytic speech signal, and LPC residual. Speech signals used in the experiments were corrupted by addition of white Gaussian noise whose noise levels are 10, 5, 0, and −5 [dB]. The performance was evaluated using the gross pitch error (GPE) and fine pitch error (FPE). The results demonstrate that this algorithm based on complex speech analysis can perform better than conventional methods in an extremely noisy environment.

New speech harmonic structure measure and its applications to speech processing

The harmonic structure can be easily recognized in time-frequency representation of speech signals in adverse environment. The harmonicity is a measure of the completeness of a harmonic structure. This paper presents a new harmonic structure measure that extends the conventional harmonicity to a set of harmonicities. They are expressed in terms of the grid harmonicity, the temporal harmonicity, the segment-spectral harmonicity, and the segmental harmonicity. The grid harmonicity measures the completeness of individual harmonics in each frame. The grid harmonicities in a frame are summed up to form a temporal harmonicity for representing the strength of harmonicity. The segment-spectral harmonicity, computed by summing specific grid harmonicity over a segment, evaluates the integrity of individual harmonics across a segment. The segmental harmonicity evaluates the total strength of harmonic structure within a segment. This set of harmonicities is available for a systematic analysis of the harmonic structure and effective to several speech processing tasks. The applications to speech distortion analysis, robust fundamental frequency estimation, robust voicing detection, and speech enhancement are demonstrated.

Real-time long-term prediction of ship motion for fire control applications

Based on the robust least squares wave frequency estimator, a real-time algorithm for long-term prediction of ship rolling motion is proposed for fire control applications. Simulation results using actual ship motion measurements show that the proposed scheme does not only make the prediction problem of non-stationary ship motion tractable but also enables real-time computation with good accuracy.