Mean Frequency Estimation Research Articles

Comparison of algorithms for estimation of EMG variables during voluntary isometric contractions

Many algorithms have been described in the literature for estimating amplitude, frequency variables and conduction velocity of the surface EMG signal detected during voluntary contractions. They have been used in different application areas for the non invasive assessment of muscle functions. Although many studies have focused on the comparison of different methods for information extraction from surface EMG signals, they have been carried out under different conditions and a complete comparison is not available. It is the purpose of this paper to briefly review the most frequently used algorithms for EMG variable estimation, compare them using computer generated as well as real signals and outline the advantages and drawbacks of each. In particular the paper focuses on the issue of EMG amplitude estimation with and without pre-whitening of the signal, mean and median frequency estimation with periodogram and autoregressive based algorithms both in stationary and non-stationary conditions, delay estimation for the calculation of muscle fiber conduction velocity.

Velocity Biases of Adaptive Filter Estimates in Heterodyne Doppler Lidar Measurements

Abstract Frequency estimates by heterodyne Doppler lidar (HDL) may result in velocity bias due to the atmospheric speckle effect and an asymmetrical power spectrum of the probing pulse, as discussed in a previous paper by Dabas et al. In this paper, it has been shown that the velocity bias can be accounted for and corrected on a single measurement basis for a mean frequency estimator (e.g., pulse pair). In the present paper, a new procedure is proposed and validated for adaptive filters (e.g., Levin, notch, etc.), which accounts for nonstationary conditions such as wind turbulence, wind shear, and backscattered power gradient. The present study is conducted using both numerical simulations and actual data taken by a 10-μm HDL.

Non-stationary Myoelectric Signals and Muscle Fatigue

A mathematical derivation for the mean frequency of a myoelectric signal (MES) is provided based on an amplitude modulation model for non-stationary MES. With this derivation, it is shown that mean frequency estimates of stationary and non-stationary myoelectric signals theoretically are not significantly different in a physiologically practical context. While this prediction is confirmed via a computer simulation, it is refuted with empirical evidence. Regardless, it is shown in a final study that mean frequency is capable of tracking a downward shift in the power spectrum with fatigue even in non-stationary myoelectric signals.

Chirp-Induced Bias in Velocity Measurements by a Coherent Doppler CO2Lidar

Radial wind velocity measurements by a pulsed CO2 Doppler lidar may be biased even in stationary atmospheric conditions. The authors show it is due to random speckle fluctuations of the backscattered signal and is related to the dissymmetry of the transmitted laser pulse periodogram. A procedure is proposed to correct for the bias on a shot-to-shot basis when a pulse-pair mean-frequency estimator is used for processing. The procedure is validated on simulated and actual lidar signals.

Maximum entropy digital signal processing for acoustic Doppler imaging

A maximum-entropy algorithm is developed for real time estimation of the power spectrum mean frequency of a Doppler shifted probe. This technique is compared with a covariance argument approximation and performance is given in terms of noise immunity, measurement bias, and accuracy. Estimator evaluation is made from numerical results with a computer simulated signal having a Gaussian spectral density. The maximum-entropy and covariance argument algorithms are implemented on a digital signal processing microprocessor (Analog Devices ADSP2181) for comparison. The maximum entropy technique demonstrates substantial improvement over covariance processing with respect to noise immunity and exhibits no bias in the presence of band limited noise. The maximum-entropy algorithm can be implemented, without any post-processing required, using the ADSP2181 on typical acoustic Doppler signals in the frequency range between 150 and 1200 kHz by frequency down conversion to a fundamental Nyquist interval of 4 kHz.

A single bit RF domain complex cross-correlation velocity estimator for color flow mapping.

This paper evaluates the performance of a one bit mean frequency estimator to estimate blood flow velocity for ultrasound color flow mapping. This one bit mean frequency estimator, referred to as BC3 estimator, is derived from the recently introduced complex cross-correlation model (C3M) employing the full dynamic data range. The C3M velocity estimator is not suitable for application in color flow mapping because of its high hardware complexity and associated computational load. The BC3 estimator estimates the mean blood flow velocity using only two complex cross-correlation coefficients. For this purpose the latter are computed by means of a complex one bit cross-correlation operation. Each sample of the RF signals is converted into an one bit representation based on the sign of the real and imaginary part of the RF samples. A full derivation and mathematical description of the BC3 estimator is presented. In addition, a thorough performance evaluation of the BC3 estimator in comparison with the full dynamic range C3M velocity estimator is carried out by means of signal simulations to document the effect of signal to noise ratio, sample frequency and bandwidth. For the specific simulation conditions considered the standard deviation of both estimators (C3M and BC3) is comparable. The bias of the BC3 estimator appears to be a function of velocity, while the full dynamic range C3M velocity estimator exhibits no bias. The simulation results are confirmed by evaluation of data from an in vivo measurement. Taking into account the low hardware complexity and computational load in combination with the achieved precision, it may be concluded that the BC3 estimator is well suited for implementation in color flow mapping.

A radio frequency domain complex cross-correlation model to estimate blood flow velocity and tissue motion by means of ultrasound

This article introduces a mean frequency estimator based on a radio frequency (RF) domain complex cross-correlation model (C3M). The C3M estimator differs from the real cross-correlation model (CCM) estimator in two respects; it is an unbiased estimator of blood flow velocity and/or tissue motion independent of the bandwidth of the RF ultrasound signals, and it provides an estimate of the spatial bandwidth of the RF-signal. The estimators derived from the complex cross-correlation model (mean spatial frequency, mean temporal frequency, spatial bandwidth and signal-to-noise ratio) are based on three complex cross-correlation coefficients. A full derivation and mathematical description of both estimators (C3M and CCM), starting from a Gaussian model of the complex power spectral density distribution of sampled RF signals, are presented. In addition, a thorough performance evaluation of the C3M estimator in comparison with the CCM estimator is carried out by means of simulations to document the effect of signal-to-noise ratio, bandwidth and sample frequency. In the context of the specific simulation conditions considered, the quality of the C3M estimator is shown to offer the best performance (no bias, low standard deviation of the estimate). Taking into account the computational load and the robustness of the C3M estimator, it may be concluded that the C3M estimator combines high quality and modest complexity.

Comparison of Doppler signal analysis techniques for velocity waveform, turbulence and vortex measurement: A simulation study

Simulated time-varying Doppler signals incorporating bandwidth, power variation and vortex simulation have been used to compare a number of signal analysis techniques with a view to optimising the accuracy of convective velocity waveform, spectral broadening and vortex signal estimation. The shorttime Fourier transform (STFT), the autoregressive (AR) modified covariance estimator, the time-frequency pseudo-Wigner-Ville and Choi-Williams distributions and a partial stationarising algorithm were investigated for a range of some analysis parameters (such as window duration, AR model order). It was found that all methods could estimate the convective velocity waveform well and all the nonclassical methods were an improvement over the STFT for bandwidth estimation with the stationarising method giving the lowest error. For vortex measurement, using parameters that were optimum for mean frequency and bandwidth estimation, the stationarising, modified covariance, pseudo-Wigner-Ville with a 10-ms window and Choi-Williams methods gave improved performances compared with the STFT.

A time domain mean frequency estimation algorithm of two-dimensional real-time Doppler imaging system

A time domain mean frequency estimator is proposed for use in the two-dimensional real-time Doppler ultrasound blood flow imaging system. Since the frequency domain techniques require a long observation period to resolve the frequency content of the Doppler signal spectrum, it is unsuitable for real-time two-dimensional applications. Performance characteristics of the Doppler mean frequency estimator are obtained using a computer simulation, which models the Doppler signal and the signal processing network.

The effect of echo suppression on the mean velocity estimation range of the RF cross-correlation model estimator

Ultrasound systems are widely used to visualize in real-time internal stuctures and blood flow velocity distributions. The latter are estimated from the received ultrasound radio frequency (RF) signals using a mean frequency estimator, capable of estimating the temporal and spatial mean frequency within a given depth and time window (estimation window). Since ultrasound RF-signals are composed of three major signal components (reflections, scattering and noise) it is necessary to suppress the power of the reflections or reverberations (stationary echo removal) to estimate the temporal mean frequency of the signal component induced by scattering originating from red blood cells. However, the stationary echo removal filter in front of the mean frequency estimator will restrict the temporal mean frequency estimation range because the power of the signal component induced by the slowly moving blood is suppressed as well. This article describes a stationary echo removal filter, acting in the RF-domain and adaptive to the temporal mean frequency of the signal component induced by stationary or slowly moving reflections and reverberations. Furthermore, a comparison in performance of this adaptive stationary echo removal filter and several static stationary echo removal filters is presented. For direct comparison of these filter algorithms as far as the effect on the temporal mean frequency estimation range is concerned, the same signal conditions in combination with the same RF-domain mean frequency estimator were used in this comparison. It could be demonstrated that the adaptive echo removal filter, in combination with the RF-domain mean frequency estimator used, exhibits the best performance.

An adaptive approach to computing the spectrum and mean frequency of Doppler signals.

Modern ultrasound Doppler systems are facing the problem of processing increasingly shorter data sets. Spectral analysis of the strongly nonstationary Doppler signal needs to shorten the analysis window while maintaining a low variance and high resolution spectrum. Color flow imaging requires estimation of the Doppler mean frequency from even shorter Doppler data sets to obtain both a high frame rate and high spatial resolution. We reconsider these two estimation problems in light of adaptive methods. A regularized parametric method for spectral analysis as well as an adapted mean frequency estimator are developed. The choice of the adaptive criterion is then addressed and adaptive spectral and mean frequency estimators are developed to minimize the mean square error on estimation in the presence of noise. Two suboptimal spectral and mean-frequency estimators are then derived for real-time applications. Finally, their performance is compared to that of both the FFT based periodogram and the AR parametric spectral analysis for the spectral estimator, and, to both the correlation angle and the Kristoffersen's [8] estimators for the mean frequency estimator using Doppler data recorded in vitro.

An Adaptive Approach to Computing the Spectrum and Mean Frequency of Doppler Signals

Modern ultrasound Doppler systems are facing the problem of processing increasingly shorter data sets. Spectral analysis of the strongly nonstationary Doppler signal needs to shorten the analysis window while maintaining a low variance and high resolution spectrum. Color flow imaging requires estimation of the Doppler mean frequency from even shorter Doppler data sets to obtain both a high frame rate and high spatial resolution. We reconsider these two estimation problems in light of adaptive methods. A regularized parametric method for spectral analysis as well as an adapted mean frequency estimator are developed. The choice of the adaptive criterion is then addressed and adaptive spectral and mean frequency estimators are developed to minimize the mean square error on estimation in the presence of noise. Two suboptimal spectral and mean-frequency estimators are then derived for real-time applications. Finally, their performance is compared to that of both the FFT based periodogram and the AR parametric spectral analysis for the spectral estimator, and, to both the correlation angle and the Kristoffersen′s [8] estimators for the mean frequency estimator using Doppler data recorded in vitro.

Bias in mean frequency estimation of Doppler signals due to wall clutter filters

Wall clutter filters used in Doppler ultrasound systems give rise to a bias in the mean frequency estimation. This effect has been explored for two second order filters: the initialised infinite impulse response (IIR)-type filter, and the finite impulse response (FIR) echo-canceller filter. These are used in conjunction with two mean frequency estimation algorithms: the FFT-based intensity-weighted-mean algorithm, and the autocorrelation algorithm. The bias is shown to be caused by the finite settling times of the filters. The IIR filter, although having a much better frequency response than the FIR filter, has a greater bias associated with it. A compromise between bias and frequency response is suggested and a simple method of bias correction is described.

A noninvasive method to estimate wall shear rate using ultrasound

Wall shear stress (blood viscosity × wall shear rate), imposed by the flowing blood, and blood pressure are the main mechanical forces acting on a blood vessel wall. Accurate measurement of wall shear stress is important when investigating the development of vascular disease, since both high and low wall shear stresses have been cited as factors leading to vessel wall anomalies. Furthermore, in vitro studies have shown that endothelial cells, which play a key role in the function of the underlying arterial wall, undergo a variety of structural and functional changes in response to imposed shear stress. However, there is practically no knowledge about the influence of wall shear stress on the arterial wall in vivo because of the difficulty in measuring this stress in terms of magnitude and time variation. The method presented in this article to measure the time-dependent wall shear rate in the main arteries is based on the evaluation of velocity profiles determined by means of ultrasound, using off-line signal processing. Pulsed ultrasound is well suited for this application since it is noninvasive. The processing performed in the radio-frequency (RF) domain consists of a mean frequency estimator preceded by an adaptive vessel wall filter. In a pilot study (30 measurements in the carotid artery of five healthy volunteers) we investigated the reproducibility of our method to estimate wall shear rate as compared with the reproducibility of the measurement of blood flow velocity in the middle of the vessel. The coefficient of variation was on the order of 9% for blood flow velocity estimation, and for wall shear rate estimation on the order of 5%.

Performance of Mean-Frequency Estimators for Doppler Radar and Lidar

The performance of mean-frequency estimators for Doppler radar and lidar measurements of winds is presented in terms of two basic parameters: Φ, the ratio of the average signal energy per estimate to the spectral noise level; and Ω, which is proportional to the number of independent samples per estimate. For fixed Φ and Ω, the Cramer-Rao bound (CRB) (theoretical best performance) for unbiased estimators of mean frequency (normalized by the spectral width of the signal), signal power, and spectral width are essentially independent of the number of data samples M. For Φ, the estimators of mean frequency are unbiased and the performance is independent of M. The spectral domain estimators and covariance based estimators are bounded by the approximate periodogram CRB. The standard deviation of the maximum-likelihood estimator approaches the exact CRB, which can be more than a factor of 2 better than the performance of the spectral domain estimators or covariance-based estimators for typical Ω. For small Φ, the estimators are biased due to the effect of the uncorrelated noise (white noise), which results in uniformly distributed “bad” estimates. The fraction of bad estimates is a function of Φ and M with weak dependence on the parameter Ω. Simple empirical models describe the standard deviation of the good estimates and the fraction of bad estimates. For Doppler lidar and for large Φ, better performance is obtained by using many low-energy pulses instead of one pulse with the same total energy. For small Φ, the converse is true.

A new adaptive mean frequency estimator: application to constant variance color flow mapping

A class of adapted mean frequency estimators is proposed for color flow mapping. These estimators can be fitted to the specific characteristics of a given Doppler signal to optimize the compromise between the range of analysable frequencies and the variance of mean frequency estimation. A sub-optimal estimator is derived for real-time applications, and an adaptive criterion based on the Doppler signal variance is developed for color flow mapping applications. Its performance is compared to that of the usual correlation phase estimator on simulated Doppler signals and on synthetic Doppler images. An improvement in image quality is achieved, mainly for low signal-to-noise ratio Doppler signals.

A parallel architecture for the Color Doppler flow technique in ultrasound imaging

In this paper we present an algorithm and an architecture for the computation of the mean frequency and the variance of a Doppler signal for the implementation fo the Color Doppler Flow technique. The Color Doppler Flow is used to simplify the analysis of an echo- cardiographic image coding the blood velocity with a pseudo-color level, derived from the mean frequency of the Doppler echos. Hence, we have to perform an accurate spectral analysis of the signal to obtain careful results, but we also have to respect strict real-time constraints. We propose to use an AR algorithm for the spectral estimation, exploiting an a priori knowledge about the shape of the spectrum of the Doppler signal. We also apply the same knowledge to simplify the mean frequency estimation, avoiding the time-consuming operation of integral computations, that is replaced with the evaluation of a maximum. In this case, we show that the resulting architecture is much less expensive, with a comparable accuracy. A first result of the research has been the design of a parallel architecture for the Color Doppler Flow, composed of 64 DSPs organized on four boards of 16 DSPs each.

A comparison method for mean frequency estimators for Doppler ultrasound.

Mean frequency estimators as used in pulsed Doppler ultrasound equipment should provide an accurate (quality) and consistent (robustness) estimate over a wide range of signal conditions. In a simplified signal model, the main parameters to consider are the noise level, mean frequency, bandwidth and power of both the Doppler signal and the stationary component over a given time window. It may be expected that one estimator for a given parameter combination exhibits a good performance while another estimator for the same parameter combination behaves poorly. To allow direct comparison between different types of frequency estimators, a method is introduced to evaluate the quality and robustness of estimators for a common signal space covering a wide range of realistic parameter combinations. The method is illustrated using three different mean frequency estimators: (1) a first order autoregressive estimator in combination with a stationary echo filter; (2) a second order autoregressive estimator; and (3) a complex linear regression estimator in combination with a stationary echo filter. It is concluded that, for the parameter combination considered, the complex linear regression estimator exhibits the best quality (low variance and bias of the estimate) and robustness (consistent quality for all parameter combinations).

A comparison method for mean frequency estimators for Doppler ultrasound

Mean frequency estimators as used in pulsed Doppler ultrasound equipment should provide an accurate (quality) and consistent (robustness) estimate over a wide range of signal conditions. In a simplified signal model, the main parameters to consider are the noise level, mean frequency, bandwidth and power of both the Doppler signal and the stationary component over a given time window. It may be expected that one estimator for a given parameter combination exhibits a good performance while another estimator for the same parameter combination behaves poorly. To allow direct comparison between different types of frequency estimators, a method is introduced to evaluate the quality and robustness of estimators for a common signal space covering a wide range of realistic parameter combinations. The method is illustrated using three different mean frequency estimators: (1) a first order autoregressive estimator in combination with a stationary echo filter; (2) a second order autoregressive estimator; and (3) a complex linear regression estimator in combination with a stationary echo filter. It is concluded that, for the parameter combinations considered, the complex linear regression estimator exhibits the best quality (low variance and bias of the estimate) and robustness (consistent quality for all parameter combinations).

Estimation of mean frequency and variance of ultrasonic Doppler signal by using second-order autoregressive model

In order to estimate the mean frequency and variance of the diagnostic ultrasound Doppler signal in the presence of clutter noise, a new estimator using a second-order autoregressive (AR) model, called the AR estimator, is proposed. The sampled signal that contains information of both the Doppler signal and clutter is described by the second-order AR model with two poles. The mean frequency and variance of a unidirectional Doppler signal can be estimated, respectively, from the phase and the magnitude of the pole, with larger phase between the two poles. If the clutter is not completely rejected, all conventional estimators, including the autocorrelation (AC) estimator, result in erroneous estimations for the mean frequency and variance of the Doppler signal, whereas the AR estimator gives an accurate estimation. In the absence of clutter, however, the performance of both the AC and AR estimators are similar. If the blood flows in both directions in a sample volume and the clutter is rejected to the extent that it no longer obscures the Doppler signal, the proposed method can estimate simultaneously the mean frequencies and variances of both the forward and reverse blood flows. The performance of the proposed AR estimator was compared with that of the AC estimator by computer simulations and experiments, and it was found that when the number of available sampled data is small, the AR estimator does not require the use of a clutter filter, which simplifies Doppler signal detection.