Performance of short-time spectral parametric methods for reducing the variance of the Doppler ultrasound mean instantaneous frequency estimation

To achieve an accurate estimation of the instantaneous turbulent velocity fluctuations downstream of prosthetic heart valves in vivo, the variability of the spectral method used to measure the mean frequency shift of the Doppler signal (i.e. the Doppler velocity) should be minimised. This paper investigates the performance of various short-time spectral parametric methods such as the short-time Fourier transform, autoregressive modelling based on two different approaches, autoregressive moving average modelling based on the Steiglitz-McBride method, and Prony's spectral method. A simulated Doppler signal was used to evaluate the performance of the above mentioned spectral methods and Gaussian noise was added to obtain a set of signals with various signal-to-noise ratios. Two different parameters were used to evaluate the performance of each method in terms of variability and accurate matching of the theoretical Doppler mean instantaneous frequency variation within the cardiac cycle. Results show that autoregressive modelling outperforms the other investigated spectral techniques for window lengths varying between 1 and 10 ms. Among the autoregressive algorithms implemented, it is shown that the maximum entropy method based on a block data processing technique gives the best results for a signal-to-noise ratio of 20 dB. However, at 10 and 0 dB, the Levinson-Durbin algorithm surpasses the performance of the maximum entropy method. It is expected that the intrinsic variance of the spectral methods can be an important source of error for the estimation of the turbulence intensity. The range of this error varies from 0.38% to 24% depending on the parameters of the spectral method and the signal-to-noise ratio.     

Simulation of nonstationary spectral analysis of turbulence in the aorta using a modified autoregressive or maximum entropy (AR/ME) method

A new method of parametric spectral calculation based on the ensemble average technique, which is a natural expansion of the Burg's maximum entropy method, is proposed. This method is applied to a set of numerical simulation data which simulate turbulent velocity fluctuations data measured in the canine aorta with a hot-film anemometer. The autoregressive order of the spectral calculation is chosen by the minimum AIC (Akaike's information criteria) method. It is shown that the proposed method used with the minimum AIC method has a very good performance calculating smooth averaged spectra in the short-time quasisteady spectral analysis of nonstationary processes such as turbulence in the aorta.     

Selection of a spectral analysis method for the assessment of velocity distribution based on the spectral distribution of ultrasonic Doppler signals

The direct Fourier transform method, autoregressive modelling, the maximum likelihood method and the Wigner-Ville distribution were applied to the Doppler signal obtained from a fully insonated laminar model flow. The appreciation of the spectral method was based on the properties of the ratio variance/(f_mean)² (INT) of the spectrum. The basic criterion was the sensitivity of INT to the analysis parameters, especially the data window. The results of spectral analysis, as well as the properties of INT, were strongly affected by the method applied. The maximum likelihood method appeared best suited for the purpose of assessment of velocity distribution and is expected to give the best results in the case of in vivo blood flow. The performances of other discussed methods were inferior, due to their stronger incompatibility with the signal properties.     

Effect of method and parameters of spectral analysis on selected indices of simulated Doppler spectra

The sensitivity of Doppler spectral indices (mean frequency, maximum frequency, spectral broadening index and turbulence intensity) to the conditions of spectral analysis (estimation method, data window, smoothing window or model order) increases with decreasing signal bandwidth and growing index complexity. The bias of spectral estimate has a more important effect on these indices than its variance. A too low order, in the case of autoregressive modelling and minimum variance methods, and excessive smoothing, in the case of the FFT method, result in increased errors of Doppler spectral indices. There is a trade-off between the errors resulting from a short data window and those due to insufficient temporal resolution.     

Smoothed power spectrum estimate applied for analysis of the doppler signal from blood flow

A simple method for the improvement of the definition of the instantaneous spectrum estimate of Doppler signal is proposed. A short review of the stochastical properties of FFT spectrum estimates is presented. This review allowed us to develop a concept of the 'estimation noise' as an interpretation of the stochastic uncertainty of the estimation. This, in turn, permitted us to propose a method of adaptive filtering of spectral estimation to minimise the effects of the 'estimation noise'. Proposed filtering in the frequency domain corresponds to a procedure known as smoothing of the estimate. Two different smoothing procedures are presented: classical, linear smoothing and nonlinear, homomorphic smoothing. The performances of the smoothed spectrum estimate are theoretically and experimentally studied, showing that their effectiveness depends mostly on the shape of the Doppler spectrum. Although smoothing always reduces the spectral resolution, the important limitation of the variance of estimation can be achieved without meaningful deterioration of the resolution in our application. Thus, the proposed procedures may sensibly improve the accuracy of the relationship between the shape of the spectrum and the flow parameters. As a result, more exact determination of flow characteristics such as stability or maximum velocity, even in cases of low signal-to-noise power ratio, should be possible.     

包含离散谱线的电生理信号的参数模型谱估计问题

参数模型谱估计是的这二十多年来得到词发展的现代谱估计方法。根据极大熵原理，ＡＲ谱估计受到了普遍重视。极大熵谱估计要求信号必须是具有连续谱分布函数的一般线性疗列。然而在生物医学工程中遇到的实际信号，其谱函数往往包含很尖锐的谱峰（如脑电信号的α峰），甚至包含离散谱线。实验证明，这种情况下对谱峰频率的估计仍然很精确，但对谱幅估计误差较大，国外近些年提出的一种最佳Ｂｕｒｇ修正算法，有一定的改善。我们从工程     

Time-frequency analysis of the first heart sound. Part 2: An appropriate time-frequency representation technique

A simulated first heart sound (S1) signal is used to determine the best technique for analysing physiological S1 from the following five time-frequency representations (TFR): the spectrogram, time-varying autoregressive modelling, binomial reduced interference distribution, Bessel distribution and cone-kernel distribution (CKD). To provide information on the time and frequency resolutions of each TFR technique, the instantaneous frequency and the −3 dB bandwidth as functions of time were computed for each simulated component of the S1. The performance index for selecting the best technique was based on the relative error and the correlation coefficient of the instantaneous frequency function between the theoretical distribution and the computed TFR. This index served to select the best technique. The sensitivity of each technique to noise and to small variations of the signal parameters was also evaluated. The results of the comparative study show that, although important limitations were found for all five TFRs tested, the CKD appears to be the best technique for the time-frequency analysis of multicomponent signals such as the simulated S1.     

A method for reduction of power line interference in the ECG

A method for reduction of power line interference (PLI) in electrocardiograms with sampling rate integer multiple of the nominal power line frequency is developed and tested using simulated signals and records from the databases of the American Heart Association and the Massachusetts Institute of Technology. The method involves parabolic detrending of the ECG, estimation of the signal components with frequencies corresponding to PLI by discrete Fourier transform, and minimum-squared-error approximation of decimated series of averaged instantaneous values of PLI using appropriately defined weights. Tests of the proposed method with simulated data show that for signal-to-noise ratios SNR greater than 25 dB, the logarithmic relative error is below −32 dB and the error-to-signal ratio is less than −24 dB. For lower SNR, the errors increased, and a noise attenuation of 0.6 dB is observed. The main advantage of the developed method in comparison with other simpler and faster approaches is the accurate interference reduction in cases when the power line frequency deviates from the nominal 50 or 60 Hz. Due to computational burden, the method is more suitable for off-line application, but real-time implementation, using modern processors, is also possible.     

Noise reduction in Doppler ultrasound signals using an adaptive decomposition algorithm

A novel de-noising method for improving the signal-to-noise ratio (SNR) of Doppler ultrasound blood flow signals, called the matching pursuit method, has been proposed. Using this method, the Doppler ultrasound signal was first decomposed into a linear expansion of waveforms, called time-frequency atoms, which were selected from a redundant dictionary named Gabor functions. Subsequently, a decay parameter-based algorithm was employed to determine the decomposition times. Finally, the de-noised Doppler signal was reconstructed using the selected components. The SNR improvements, the amount of the lost component in the original signal and the maximum frequency estimation precision with simulated Doppler blood flow signals, have been used to evaluate a performance comparison, based on the wavelet, the wavelet packets and the matching pursuit de-noising algorithms. From the simulation and clinical experiment results, it was concluded that the performance of the matching pursuit approach was better than those of the DWT and the WPs methods for the Doppler ultrasound signal de-noising.     

Selection of optimal AR spectral estimation method for EEG signals using Cramer-Rao bound

Electroencephalography is an essential clinical tool for the evaluation and treatment of neurophysiologic disorders related to epilepsy. Careful analyses of the electroencephalograph (EEG) records can provide valuable insight and improved understanding of the mechanisms causing epileptic disorders. The detection of epileptiform discharges in the EEG is an important element in the diagnosis of epilepsy. In this study, EEG signals recorded from 30 subjects were processed using autoregressive (AR) method and EEG power spectra were obtained. The parameters of autoregressive method were estimated by different methods such as Yule-Walker, covariance, modified covariance, Burg, least squares, and maximum likelihood estimation (MLE). EEG spectra were then used to analyze and characterize epileptiform discharges in the form of 3-Hz spike and wave complexes in patients with absence seizures. The variations in the shape of the EEG power spectra were examined in order to obtain medical information. These power spectra were then used to compare the applied methods in terms of their frequency resolution and determination of epileptic seizure. The Cramer-Rao bounds (CRB) were derived for the estimated AR parameters of the EEG signals and the performance evaluation of the estimation methods was performed using the CRB values. Finally, the optimal AR spectral estimation method for the EEG signals was selected according to the computed CRB values. According to the computed CRB values, the performance characteristics of the MLE AR method was found extremely valuable in EEG signal analysis.     

Adaptive spectral analysis of cutaneous electrogastric signals using autoregressive moving average modelling

The recording of the human, gastric myoelectrical activity, by means of cutaneous electrodes is called electrogastrography (EGG). It provides a noninvasive method of studying electrogastric behaviour. The normal frequency of the gastric signal is about 0·05 Hz. However, sudden changes of its frequency have been observed and are generally considered to be related to gastric motility disorders. Thus, spectral analysis, especially online spectral analysis, can serve as a valuable tool for practical purposes. The paper presents a new method of the adaptive spectral analysis of cutaneous electrogastric signals using autoregressive moving average (ARMA) modelling. It is based on an adaptive ARMA filter and provides both time and frequency information of the signal. Its performance is investigated in comparison with the conventional FFT-based periodogram method. Its properties in tracking time-varying instantaneous frequencies are shown. Its applications to the running spectral analysis of cutaneous electrogastric signals are presented. The proposed adaptive ARMA spectral analysis method is easy to implement and is efficient in computations. The results presented in the paper show that this new method provides a better performance and is very useful for the online monitoring of cutaneous electrogastric signals.     

Advances in processing of surface myoelectric signals: Part 1

During sustained voluntary or electrically elicted muscle contractions the surface myoelectric signal is nonstationary and it undergoes progressive changes reflecting the modifications of the motor unit action potentials and their propagation velocity. In particular, during sustained electrical stimulation, the evoked signals show progressive amplitude, time scaling and shape modification. The quantitative evaluation of these changes is important for non-invasive muscle characterisation and may be performed in either the time or frequency domain using parametric and nonparametric spectral analysis as well as alternative methodologies. The paper introduces the detection techniques, reviews and compares the methods of spectral estimation based on FFT and autoregressive models, and discusses their applications and limitations in extracting information from the surface myoelectric signal with particular regard to myoelectric manifestations of localised muscle fatigue during sustained contractions.     

On the instantaneous measurement of bloodflow by ultrasonic means

Part of the problem of determining the flow through a blood vessel is the measurement of the instantaneous average blood velocity over a cross-section of the vessel. In this paper a new method is described to estimate that velocity from the received signal of a Doppler flowmeter using continuous ultrasound. The method is based on the determination of the frequency shift averaged over the power density spectrum of the received signal. Due to a new type of instrumentation this can be done without carrying through a complete frequency analysis of that signal. This provides a rather accurate determination of the instantaneous value of the blood velocity.     

Correction for broadening in Doppler blood flow spectrum estimated using wavelet transform

The conventionally used spectral estimation technique for Doppler blood flow signal analysis is short-time Fourier transform (STFT). But this method requires stationarity of the signal during the window interval. Wavelet transform (WT), which has a flexible time-frequency window, is particularly suitable for nonstationary signals. In recently years, the WT has been used to investigate its advantages and limitations for the analysis of Doppler blood flow signals. In these studies, the estimated spectral width of Doppler blood flow signals using the WT might include significant window and nonstationarity broadening errors. These broadening errors of the time-varying spectrum were clearly undesirable since it would tend to mask the effect of flow disturbance on the spectra width. In this paper, a closed form expression for window and nonstationary root-mean-squared (rms) spectral width is given when using the WT to estimate the Doppler blood flow spectrum. The increases in the rms spectral width can be calculated and then the spectral width estimation based on the WT can be corrected.     

Measurement of the dynamics of arteriolar diameter

The diameter of the arteriolar vessels of the microcirculation undergoes a continuous variation as a consequence of vasomotion. The quantification of this process requires the implementation of spectral analysis techniques that model short data records of a finite number of superposed sinusoidal waveforms. The following techniques were tested with artificially synthetized records and actual data: the fast Fourier transform, the high-resolution autoregressive method, the maximum entropy method, and the Prony Spectral Line Estimator (PSLE). It was found that the PSLE provides the most accurate estimation of the spectral components of the dynamics of diameter changes because it does not require any assumption on the nature of the data outside the interval under analysis. This research was supported by USPHS HL 12493 and HL 17421.     

Sampling rate and the estimation of ensemble variability for repetitive signals

The measurement of ensemble variability in time-aligned event signals is studied in relation to sampling rate requirements. The theoretical analysis is based on statistical modelling of time misalignment in which the time resolution is limited by the length of the sampling interval. For different signal-to-noise ratios (SNRs), the sampling rate is derived which limits the misalignment effect to less than 10% of the noise effect. Each signal is assumed to be corrupted by additive noise. Using a normal QRS complex with a high SNR (≈ 30 dB), a sampling rate of approximately 3 kHz is needed for accurate ensemble variability measurements. This result is surprising since it implies that the Nyquist rate is far too low for accurate variability measurements. The theoretical results are supplemented with results obtained from an ECG database of 94 subjects for which the ensemble variability is computed at different sampling rates using signal interpolation. The ensemble variability is substantially reduced (40%) when increasing the rate from 1 to 3 kHz, thus corroborating the results suggested by the theoretical analysis.     

Bayesian filtering of myoelectric signals

Surface electromyography is used in research, to estimate the activity of muscle, in prosthetic design, to provide a control signal, and in biofeedback, to provide subjects with a visual or auditory indication of muscle contraction. Unfortunately, successful applications are limited by the variability in the signal and the consequent poor quality of estimates. I propose to use a nonlinear recursive filter based on Bayesian estimation. The desired filtered signal is modeled as a combined diffusion and jump process and the measured electromyographic (EMG) signal is modeled as a random process with a density in the exponential family and rate given by the desired signal. The rate is estimated on-line by calculating the full conditional density given all past measurements from a single electrode. The Bayesian estimate gives the filtered signal that best describes the observed EMG signal. This estimate yields results with very low short-time variability but also with the capability of very rapid response to change. The estimate approximates isometric joint torque with lower error and higher signal-to-noise ratio than current linear methods. Use of the nonlinear filter significantly reduces noise compared with current algorithms, and it may therefore permit more effective use of the EMG signal for prosthetic control, biofeedback, and neurophysiology research.     

基于自相关约束的信号波形估计及其在诱发电位提取中的应用

从观测数据中估计源信号的波形一直是信号处理领域中的一个重要问题.利用源信号的时间自相关函数构造一个非线性方程组,借助大规模数值计算方法,把原来直接估计源信号这样一个较困难的问题,转化为估计迭代初始值与源信号时间自相关函数的问题.使用小波模极大值法,估计迭代初始值与源信号时间自相关函数,再对方程组迭代求解,收敛后的结果即为对源信号的估计.将该方法应用于诱发电位的单通道、单次提取实验,在信噪比为0 dB时,提取结果与源信号的相关系数约为0.93,对幅度与潜伏期的估计都比较准确.实验结果表明,算法性能受迭代初始值估计精度与源信号时间自相关函数估计精度的影响,受前者影响较小,而受后者的影响相对较大.     

Review of the methods of determination of directed connectivity from multichannel data

The methods applied for estimation of functional connectivity from multichannel data are described with special emphasis on the estimators of directedness such as directed transfer function (DTF) and partial directed coherence. These estimators based on multivariate autoregressive model are free of pitfalls connected with application of bivariate measures. The examples of applications illustrating the performance of the methods are given. Time-varying estimators of directedness: short-time DTF and adaptive methods are presented.     

Determination of carotid disease with the application of STFT and CWT methods

In this study, Doppler signals were recorded from the output of carotid arteries of 40 subjects and transferred to a personal computer (PC) by using a 16-bit sound card. Doppler difference frequencies were recorded from each of the subjects, and then analyzed by using short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) methods to obtain their sonograms. These sonograms were then used to determine the relationships of applied methods with medical conditions. The sonograms that were obtained by CWT method gave better results for spectral resolution than the STFT method. The sonograms of CWT method offer net envelope and better imaging, so that the measurement of blood flow and brain pressure can be made more accurately. Simultaneously, receiver operating characteristic (ROC) analysis has been conducted for this study and the estimation performance of the spectral resolution for the STFT and CTW has been obtained. The STFT has shown a 80.45% success for the spectral resolution while CTW has shown a 89.90% success.