Mean Frequency Estimation Research Articles

Breaking the Communication-Privacy-Accuracy Trilemma

Two major challenges in distributed learning and estimation are 1) preserving the privacy of the local samples; and 2) communicating them efficiently to a central server, while achieving high accuracy for the end-to-end task. While there has been significant interest in addressing each of these challenges separately in the recent literature, treatments that simultaneously address both challenges are still largely missing. In this paper, we develop novel encoding and decoding mechanisms that simultaneously achieve optimal privacy and communication efficiency in various canonical settings. In particular, we consider the problems of mean estimation and frequency estimation under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -local differential privacy and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula> -bit communication constraints. For mean estimation, we propose the SQKR mechanism, a scheme based on Kashin’s representation and random sampling, with order-optimal estimation error under both constraints. We further apply SQKR to distributed SGD and obtain a communication efficient and (locally) differentially private distributed SGD protocol. For frequency estimation, we present the RHR mechanism, a scheme that leverages the recursive structure of Walsh-Hadamard matrices and achieves order-optimal estimation error for all privacy levels and communication budgets. As a by-product, we also construct a distribution estimation mechanism that is rate-optimal for all privacy regimes and communication constraints, extending recent work that is limited to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b=1$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon =O(1)$ </tex-math></inline-formula> . Our results demonstrate that intelligent encoding under joint privacy and communication constraints can yield a performance that matches the optimal accuracy achievable under either constraint alone. In other words, the optimal performance is determined by the more stringent of the two constraints, and the less stringent constraint can be satisfied for free.

Two-Step Frequency Estimation of GNSS Signal in High-Dynamic Environment

To improve frequency accuracy which is affected by two parameters in high-dynamic acquisition, we propose a two-step frequency estimation method based on the mean frequency (MF) model for high-dynamic parameters estimation. The first step is based on the discrete chirp-Fourier transform (DCFT) for coarse MF estimation, where the MF accuracy and frequency search step are derived. In the second step, the maximum likelihood estimation process (MLEP) is adopted for fine MF estimation. Compared with state-of-art methods, it is verified that the two-step method can improve the detection probability in coarse MF estimation and improve the MF accuracy with low computational burdens under conditions with a moderate signal-to-noise ratio (SNR).

Estimation of mean and median frequency from synthetic sEMG signals: Effects of different spectral shapes and noise on estimation methods

The detection of electrical signs of muscle fatigue passes through the choice of appropriate spectral estimation techniques for the extraction of parameters such as Mean and Median Frequency from surface myoelectric signals. Unfortunately, despite the huge number of contributions using various spectral techniques to process signals recorded in fatiguing protocols, there is no agreement on the method that works best, and to our knowledge, the performance of the estimation techniques has been evaluated only on a limited range of spectral shapes. To study the fatigue phenomenon, it is important to consider the range of variation of the spectral parameters and then the different shapes assumed by the signal spectrum. In this work, the latter characteristics have been used to simulate synthetic myoelectric signals whose Power Spectral Density has been estimated in different noise conditions by using the following techniques: a) indirect technique by the estimation of the autocorrelation function; b) direct technique by the Welch estimation method with special attention to the window functions for signal segmentation; c) Burg autoregressive approach with special attention to the model order. The main result, after assessing that Burg’s approach outperforms all the other techniques for all the examined conditions, outlines that the model’s order, despite ranging between 6 and 12, depends on the spectral shape and affects the estimation of the Median Frequency. This partially overwrites previous results of the literature and provides the useful recommendation to choose, among the spectral estimation techniques, the most adaptive to the dynamics of the fatigue process.

Mean local frequency-wavenumber estimation through synthetic time-reversal of diffuse Lamb waves

Inspection of the elastic properties of plate-like structures is an important and challenging problem in many engineering disciplines. There exist multiple non-destructive inspection techniques based on active ultrasonic transducers to tackle this problem. In recent years, the usefulness of passively induced waves has also been explored. It has been shown that the diffuse waves, often referred to as coda waves, carry profound information about the elastic properties of the supporting medium. They can effectively probe the volume of a medium due to multiple scattering and long propagation paths. Moreover, the measured diffuse field can be synthetically focused using the correlation of wavefield’s time histories. The local elastic properties of the medium can be inferred from the focal spot size.In this work, we demonstrate the algorithm of mean local frequency-wavenumber estimation through synthetic focusing of diffuse Lamb waves. We provide theoretical foundations for expanding the concept of mean frequency estimation in purely temporal signals to mean wavenumber estimation in a spatiotemporal Lamb wave field. The applicability of this approach for the damage detection in plate-like structures is demonstrated on aluminum and carbon fiber reinforced polymer (CFRP) plates with localized defects. Test samples are excited with sequences of white noise signals, to create optimal diffuse field conditions, and wavefield is captured using a Scanning Laser Doppler Vibrometer (SLDV). We show that the spatial maps of mean wavenumber allow for precise localization and sizing of damage.

Evaluation of disbonds at various interfaces of adhesively bonded aluminum plates using all-optical excitation and detection of zero-group velocity Lamb waves

Inspection of adhesively bonded metallic plates, commonly used in aircraft structures, remains challenging for modern non-destructive testing (NDT) techniques. When a probing ultrasound (US) wave interacts with the plate boundaries, it produces multiple propagating guided waves (or Lamb modes). Analysis of these waves can be complicated due to a strong geometrical dispersion. However, recent studies showed that for specific frequencies zero-group velocity (ZGV) modes exist. Any changes in a bounded structure, like delaminations, drastically alter the conditions for zero-group velocity waves, thus making this method highly sensitive for NDT applications. Laser ultrasound (LU) provides a very broad bandwidth of the generated waves, thus it is a feasible tool for a spectroscopy-based investigation of the ZGV modes. In this paper, we demonstrate an application of high-repetition rate LU with a non-contact fiber-optic Sagnac interferometer on receive for high resolution imaging of delaminations in a structure consisting of 3 epoxy-bonded aluminum plates. The investigation is supported by numerical analysis of Lamb waves existing in the structure to determine ZGV modes sensitive to delaminations at particular bonding interfaces. Tracking the selected modes permits imaging and identification of defects. We also show that mean frequency estimation of the ZGV modes can improve the contrast-to-noise ratio compared to an amplitude of the single ZGV frequency.

Using mean frequency estimation algorithms for unambiguous identification and visualization of an acoustically active catheter

Minimally invasive procedures using ultrasound are becoming prominent, especially in applications like biopsy, catheter guidance, and surgeries. In our previous work a catheter tip is fitted with a miniature omnidirectional piezoelectric crystal; the ultrasonic field from the imaging array and the piezoelectric crystal interact resulting in a symmetric Doppler shift. Previously, a frequency domain algorithm was used to identify pixels having the symmetric Doppler shift. The identified pixels can then be visualized on B-mode and color map with a unique color thus representing the location of the catheter tip. However, frequency domain algorithms are computationally expensive and require changes to data workflow. Using mean frequency estimators with symmetric Doppler shift results in the catheter tip being displayed as zero mean noise making it hard to distinguish from color Doppler noise. To overcome this limitation, complex demodulation can be used. Modulating the time domain signal with sine and cosine by the piezoelectric excitation frequency and summing them up results in cancellation of one of the symmetric Doppler components. With only one frequency component remaining mean frequency estimators can be used to identify the location of the catheter. The presented algorithm has lower computational complexity and requires minimal change in software design.

Reconstructing Tone Sequences from Functional Magnetic Resonance Imaging Blood-Oxygen Level Dependent Responses within Human Primary Auditory Cortex.

Here we show that, using functional magnetic resonance imaging (fMRI) blood-oxygen level dependent (BOLD) responses in human primary auditory cortex, it is possible to reconstruct the sequence of tones that a person has been listening to over time. First, we characterized the tonotopic organization of each subject’s auditory cortex by measuring auditory responses to randomized pure tone stimuli and modeling the frequency tuning of each fMRI voxel as a Gaussian in log frequency space. Then, we tested our model by examining its ability to work in reverse. Auditory responses were re-collected in the same subjects, except this time they listened to sequences of frequencies taken from simple songs (e.g., “Somewhere Over the Rainbow”). By finding the frequency that minimized the difference between the model’s prediction of BOLD responses and actual BOLD responses, we were able to reconstruct tone sequences, with mean frequency estimation errors of half an octave or less, and little evidence of systematic biases.

Long-range wind monitoring in real time with optimized coherent lidar

Two important enabling technologies for pulsed coherent detection wind lidar are the laser and real-time signal processing. In particular, fiber laser is limited in peak power by nonlinear effects, such as stimulated Brillouin scattering (SBS). We report on various technologies that have been developed to mitigate SBS and increase peak power in 1.5-μm fiber lasers, such as special large mode area fiber designs or strain management. Range-resolved wind profiles up to a record range of 16 km within 0.1-s averaging time have been obtained thanks to those high-peak power fiber lasers. At long range, the lidar signal gets much weaker than the noise and special care is required to extract the Doppler peak from the spectral noise. To optimize real-time processing for weak carrier-to-noise ratio signal, we have studied various Doppler mean frequency estimators (MFE) and the influence of data accumulation on outliers occurrence. Five real-time MFEs (maximum, centroid, matched filter, maximum likelihood, and polynomial fit) have been compared in terms of error and processing time using lidar experimental data. MFE errors and data accumulation limits are established using a spectral method.

Fourier-Based Feature Extraction for Classification of EEG Signals Using EEG Rhythms

In this paper, we propose a method for the analysis and classification of electroencephalogram (EEG) signals using EEG rhythms. The EEG rhythms capture the nonlinear complex dynamic behavior of the brain system and the nonstationary nature of the EEG signals. This method analyzes common frequency components in multichannel EEG recordings, using the filter bank signal processing. The mean frequency (MF) and RMS bandwidth of the signal are estimated by applying Fourier-transform-based filter bank processing on the EEG rhythms, which we refer intrinsic band functions, inherently present in the EEG signals. The MF and RMS bandwidth estimates, for the different classes (e.g., ictal and seizure-free, open eyes and closed eyes, inter-ictal and ictal, healthy volunteers and epileptic patients, inter-ictal epileptogenic and opposite to epileptogenic zone) of EEG recordings, are statistically different and hence used to distinguish and classify the two classes of signals using a least-squares support vector machine classifier. Experimental results, with 100 % classification accuracy, on a real-world EEG signals database analysis illustrate the effectiveness of the proposed method for EEG signal classification.

Limits to the information gain from lidar measurements.

Measurements over the return signal are an integral part of lidar remote sensing by which we gather information about the characteristics of specific targets. But how much information is gained by performing a given lidar measurement? By defining Shannon's mutual information of a lidar observation, here we consider the bits of information content on the measurement and describe mathematically the capacity of lidar estimates to represent a corresponding property in the target. For heterodyne Doppler lidars in particular, we have found simple analytical formulas that consider the information gain in mean-frequency estimates.

Features based on intrinsic mode functions for classification of EMG signals

In this paper, the features based on Intrinsic Mode Functions (IMFs) for classification of EMG signals are presented. The EMD method decomposes EMG signals into a set of narrow-band components known as IMFs. The features, namely mean frequency estimation and singular value computation, extracted from IMFs are exploited for classification of EMG signals. These parameters are used as an input to Least Squares Support Vector Machine (LS-SVM) with Radial Basis Function (RBF) for automatic classification of EMG signals. The classification accuracy for classification of normal and abnormal EMG signals obtained by the proposed method is 99.03% with RBF kernel of LS-SVM. The experimental results are presented to show the effectiveness of the proposed method for classification of normal and abnormal EMG signals (myopathy and neuropathy).

Innervation zone of the vastus medialis muscle: position and effect on surface EMG variables

The aim of this study was to investigate the position of the innervation zone (IZ) of the vastus medialis (VM) and its effect on the electromyographic (EMG) amplitude and mean frequency estimates. Eighteen healthy subjects performed maximal isometric knee extensions at three knee angles. Surface EMG signals were collected by using a 16 × 8 electrode grid placed on the VM muscle. The position of the IZ was estimated through visual analysis, and traditional bipolar signals were obtained from channels over and away from it; amplitude and mean frequency values were extracted and compared using an analysis of variance (ANOVA) with repeated measures. The IZ is shaped as a line running from the proximal–lateral to the distal–medial aspect of the VM muscle. The presence of an IZ under the electrodes lowered the EMG amplitude (P < 0.001, F = 58.11) and increased the EMG mean frequency (P < 0.001, F = 26.47); variations of these parameters due to the knee flexion angle were less frequently observed in EMG signals collected over than away from the IZ. Electrodes placed ‘over the belly of the VM muscle’ are likely to collect EMG signals influenced by the presence of the IZ, thus hindering the detection of changes in muscle activity.

Feasibility study of detecting surface electromyograms in severely obese patients

The aims of this study were to examine if surface EMG signals can be detected from the quadriceps femoris muscle of severely obese patients and to investigate if differences exist in quadriceps force and myoelectric manifestations of fatigue between obese patients and lean controls.Fourteen severely obese patients (body mass index, BMI, mean±SD: 44.9±6.3kg/m2) and fourteen healthy controls (BMI: 23.7±2.5kg/m2) were studied. The vastus medialis and lateralis of the dominant thigh were concurrently investigated during voluntary isometric contractions (10-s long at submaximal and maximal intensities and intermittent submaximal contractions until exhaustion) and sustained (120-s long) electrically elicited contractions.We found that the detection of surface EMG signals from the quadriceps is feasible also in severely obese subjects presenting increased thickness of the subcutaneous fat tissue. In addition, we confirmed and extended previous findings showing that the volume conductor properties determine the amplitude and spectral features of the detected surface EMG signals: the lower the subcutaneous tissue thickness, the higher the amplitude and mean frequency estimates. Further, we found no differences in the mechanical and myoelectric manifestations of fatigue during intermittent voluntary and sustained electrically elicited contractions between obese patients and lean controls.

Synthetic Aperture Technique Applied to Tissue Attenuation Imaging

AbstractThe attenuating properties of biological tissue are of great importance in ultrasonic medical imaging. Investigations performedin vitroandin vivoshowed the correlation between pathological changes in the tissue and variation of the attenuation coefficient. In order to estimate the attenuation we have used the downshift of mean frequency (fm) of the interrogating ultrasonic pulse propagating in the medium. To determine thefmalong the propagation path we have applied thefmestimator (I/Q algorithm adopted from the Doppler mean frequency estimation technique). The mean-frequency shift trend was calculated using Single Spectrum Analysis. Next, the trends were converted into attenuation coefficient distributions and finally the parametric images were computed. The RF data were collected in simulations and experiments applying the synthetic aperture (SA) transmit-receiving scheme. In measurements the ultrasonic scanner enabling a full control of the transmission and reception was used. The resolution and accuracy of the method was verified using tissue mimicking phantom with uniform echogenicity but varying attenuation coefficient.

초음파 도플러 컬러 유동 사상에서 신호 대 잡음비 특성의 향상

초음파 컬러 유동 사상에서 가장 많이 사용되는 Kasai 알고리듬은 래그-1 자기상관 방법으로서 적은 계산량으로 비교적 우수하게 도플러 평균주파수를 추정한다. 하지만 특히 깊은 곳을 영상화하는 경우 낮은 신호 대 잡음비로 인해 추정성능이 저하된다. 본 논문에서는 낮은 신호 대 잡음비에서도 Kasai 알고리듬보다 우수한 디에일리어스된 래그-2 자기상관방법을 제안하고 시뮬레이션을 통해 성능을 검증하였다. 제안한 방법은 잡음이 존재하는 경우 도플러 평균주파수 추정 성능을 평균 자승 오차 측면에서 전반적으로 약 2~3dB 정도 개선시켜줌을 확인하였다. 【Being the most widely used in ultrasound Doppler color flow mapping, the Kasai algorithm, also known as lag-1 autocorrelation method, is capable of estimating the Doppler mean frequency relatively accurately with a modest amount of computation. Particularly in the case of imaging deep lying areas, however, its performance suffers due to low signal-to-noise ratios. The purpose of this paper is to propose a dealiased lag-2 autocorrelation method which is superior to the Kasai algorithm even at low signal-to-noise ratios and to compare their performances through simulations. The proposed algorithm is found to be better by about 2 to 3 dB than the Kasai algorithm in terms of Doppler mean frequency estimation error in the presence of measurement noise.】

Mean frequency derived via Hilbert-Huang transform with application to fatigue EMG signal analysis

The mean frequency (MNF) of surface electromyography (EMG) signal is an important index of local muscle fatigue. The purpose of this study is to improve the mean frequency (MNF) estimation. Three methods to estimate the MNF of non-stationary EMG are compared. A novel approach based on Hilbert-Huang transform (HHT), which comprises the empirical mode decomposition (EMD) and Hilbert transform, is proposed to estimate the mean frequency of non-stationary signal. The performance of this method is compared with the two existing methods, i.e. autoregressive (AR) spectrum estimation and wavelet transform method. It is observed that our method shows low variability in terms of robustness to the length of the analysis window. The time-varying characteristic of the proposed approach also enables us to accommodate other non-stationary biomedical data analysis.

A New Approach for Estimation of Instantaneous Mean Frequency of a Time-Varying Signal

Analysis of nonstationary signals is a challenging task. True nonstationary signal analysis involves monitoring the frequency changes of the signal over time (i.e., monitoring the instantaneous frequency (IF) changes). The IF of a signal is traditionally obtained by taking the first derivative of the phase of the signal with respect to time. This poses some difficulties because the derivative of the phase of the signal may take negative values thus misleading the interpretation of instantaneous frequency. In this paper, a novel approach to extract the IF from its adaptive time-frequency distribution is proposed. The adaptive time-frequency distribution of a signal is obtained by decomposing the signal into components with good time-frequency localization and by combining the Wigner distribution of the components. The adaptive time-frequency distribution thus obtained is free of cross-terms and is a positive time-frequency distribution but it does not satisfy the marginal properties. The marginal properties are achieved by applying the minimum cross-entropy optimization to the time-frequency distribution. Then, IF may be obtained as the first central moment of this adaptive time-frequency distribution. The proposed method of IF estimation is very powerful for applications with low SNR. A set of real-world and synthetic signals of known IF dynamics is tested with the proposed method as well as with other common time-frequency distributions. The simulation shows that the method successfully extracted the IF of the signals.

Differences Among Wavelet- And Fourier-based Center Frequency Estimates With Distributional Changes In The Power Spectrum

PURPOSE To compare wavelet- and Fourier-based center frequency estimates for stationary synthetic and real EMG signals with changes in the distributional shape of the power spectrum. METHODS Ten adults (mean ± SD age=22 ± 3 yrs) performed maximal isometric muscle actions of the dominant forearm flexors. The surface EMG signal was recorded with a bipolar surface electrode arrangement placed over the biceps brachii muscle. Twenty synthetic sinusoidal signals (10 without noise; 10 with random white noise) were generated to simulate a systematic increase in the bandwidth toward the higher frequencies, which sequentially increased the positive skewness of the power spectra. Discrete Fourier transforms (DFT) were used to generate the power spectra, calculate bandwidth, and provide the mean power frequency (MPF) and median frequency (MDF) estimates. Complex continuous wavelet transforms (CWT) were used to provide average instantaneous mean frequency (AIMF) estimates. All signal synthesis and processing was done with LabVIEW 7 programming software. RESULTS Bandwidths of the synthetic signals increased toward the higher frequencies from 53–132 Hz (noise-free) and 56–136 Hz (with noise), while the bandwidth ranged from 49–170 Hz for the EMG signals. Frequency at peak spectral power was held constant at 50 Hz for the synthetic signals, but ranged from 38–92 Hz for the EMG signals. For the noise-free synthetic and EMG signals, MPF, MDF, and AIMF increased (p ≤ 0.05) with increases in bandwidth. For the synthetic signals with noise, MDF and AIMF increased (p ≤ 0.05), while MPF decreased (p ≤ 0.05) with increases in bandwidth. There were no differences (p > 0.05) between the slope coefficients for increases in MPF and MDF with increases in bandwidth, however, the slope for increases in AIMF was always lower (p ≤ 0.05). MPF was consistently the highest center frequency estimate, while AIMF was consistently the lowest and closest to the frequency at peak spectral power. CONCLUSIONS These findings indicated differences among the patterns of response for MPF, MDF, and AIMF center frequency estimates with increases in bandwidth toward higher frequencies, despite signal stationarity. Comparatively, MDF and AIMF estimates responded consistently under the modulated synthetic and EMG signal conditions, while MPF estimates responded differently, especially when simulated noise was introduced. Though MDF and AIMF estimates consistently tracked the frequency shifts, AIMF estimates were always closest to the frequency at peak spectral power, which may reflect the densest regions of the power spectrum. Overall, normalization may be necessary when reporting center frequencies.

Mean Frequency Estimation of Narrowband Signals

This letter shows that the single frequency approximation for a narrowband lowpass signal embedded in white noise using the Pisarenko harmonic decomposition algorithm is approximately the power-weighted mean frequency of the signal. Experimental results indicate that this method is superior to a commonly used Fourier transform based mean frequency estimation method.

On estimation of frequency data with censored observations

AbstractThe problem of the estimation of mean frequency of events in the presence of censoring is important in assessing the efficacy, safety and cost of therapies. The mean frequency is typically estimated by dividing the total number of events by the total number of patients under study. This method, referred to in this paper as the ‘naïve estimator’, ignores the censoring. Other approaches available for this problem require many assumptions that are rarely acceptable. These include the assumption of independence, constant hazard rate over time and other similar distributional assumptions. In this paper a simple non‐parametric estimator based on the sum of the products of Kaplan–Meier estimators is proposed as an estimator of mean frequency, and its approximate variance and standard error are derived. An illustration is provided to show the derivation of the proposed estimator. Although the clinical trial setting is used in this paper, the problem has applications in other areas where survival analysis is used and recurrent events are studied. Copyright © 2003 John Wiley &amp; Sons, Ltd.