S.I. Shah

Enhancing the precision of ECG baseline correction selective filtering and removal of residual error

Reemergence of the problem of baseline correction is related to recent advancements in the electrocardiographic (ECG) analysis of beat-to-beat repolarization changes which play an important role in risk assessment and the prediction of sudden cardiac death. These alterations often have an amplitude of a few microvolts and duration of several milliseconds and their detection requires special accuracy of baseline estimation. Using detailed analysis of various types of residual errors we designed a two-step procedure for selective filtering of ECG and removal of residual error with minimal distortion of cardiac complexes and tested this approach on 100 simulated and 210 real ECG signals. Application of this procedure provided a twofold reduction in the error of baseline estimation and T-wave amplitude measurements compared to high-pass filtering. Selective application of this approach to the segments with low baseline drift allowed analysis of low-amplitude, beat-to-beat changes in repolarization during more than 70% of the recording time.

Informative priors for minimum cross-entropy positive time-frequency distributions

A method for generating an informative prior when constructing a positive time-frequency distribution (TFD) by the method of the minimum cross-entropy (MCE) is developed. The prior is obtained from a combination of the Wigner distribution (WD) and the evolutionary periodogram, and results in a more informative MCE-TFD, as quantified via the mutual information of the distribution. The procedure allows any of the bilinear distributions to be used in the prior. Examples illustrate the performance of the new technique.

Evolutionary maximum entropy spectral analysis

We extend maximum entropy (ME) spectral analysis to non-stationary signals using the theory of the Wold-Cramer evolutionary spectrum. The evolutionary maximum entropy (EME) problem reduces to the fitting of a time-varying autoregressive model to the Fourier coefficients of the evolutionary spectrum. The model parameters are efficiently found by means of the Levinson algorithm. In the non-stationary case it is not the autocorrelation function that provides the appropriate data for the EME analysis, but rather the Fourier coefficients of the evolutionary spectrum. An estimator of these coefficients is proposed. By means of examples we show the EME estimator provides higher frequency resolution and better sidelobe behavior than existing estimators of the evolutionary spectrum.<<ETX>>

Signal synthesis and positive time–frequency distributions

Abstract A method for obtaining a generalized transfer function (GTF) of a linear time-varying system based on evolutionary spectral theory is proposed. This GTF can be used to synthesize the signal, and its magnitude squared function results in the signals positive time–frequency distribution that satisfies the marginals (i.e., a Cohen–Posch TFD). The procedure allows any prior estimate of the GTF to be modified such that the resulting posterior GTF is closest in the least square sense to the prior and satisfies the above-mentioned properties. Examples are presented to illustrate the performance of the method.

Generalized transfer function estimation using evolutionary spectral deblurring

We present a new technique for estimating the generalized transfer function (GTF) of a time-varying filter from time-frequency representations (TFRs) of its output. We use the fact that many of these representations can be written as blurred versions of the GTF. The approach consists in minimizing the error between the TFR found from the data and that found by blurring the GTF. The problem as such has many solutions. We, therefore, additionally constrain it to minimize the distance between the GTF-based spectrum and the autoterms of the Wigner distribution, suppressing the cross terms using an appropriate signal dependent mask function. To illustrate the performance of the proposed procedure we apply it to the spectral representation of speech and to signal masking and demonstrate its superior performance over the existing methods.

Evolutionary Maximum Entropy Spectral Estimation and HeartRate Variability Analysis

Spectral analysis has been used extensively in heart rate variability (HRV) studies. The spectral content of HRV signals is useful in assessing the status of the autonomic nervous system. Although most of the HRV studies assume stationarity, the statistics of HRV signals change with time due to transients caused by physiological phenomena. Therefore, the use of time-frequency analysis to estimate the time-dependent spectrum of these non-stationary signals is of great importance. Recently, the spectrogram, the Wigner distribution, and the evolutionary periodogram have been used to analyze HRV signals. In this paper, we propose the application of the evolutionary maximum entropy (EME) spectral analysis to HRV signals. The EME spectral analysis is based on the maximum entropy method for stationary processes and the evolutionary spectral theory. It consists in finding an EME spectrum that matches the Fourier coefficients of the evolutionary spectrum. The spectral parameters are efficiently calculated by means of the Levinson algorithm. The EME spectral estimator provides very good time-frequency resolution, sidelobe reduction and parametric modeling of the evolutionary spectrum. With the help of real HRV signals we show the superior performance of the EME over the earlier methods.

Autonomic nervous system effects on ventricular repolarization and RR interval variability during head-up tilt

Changes in ventricular repolarization (VR) were analyzed using 32-lead high spatial resolution ECGs (HSRE). FFT-derived low (0.04-0.15 Hz) and high (0.15-0.4 Hz) frequency powers (LF & HF, respectively) of RR interval variability (RRIV) and their ratio were used to assess changes in the autonomic activity elicited by 70/spl deg/ tilt in 9 patients with structural heart disease (SHD) and 19 control (CON) subjects. Heart rate (HR) increased with tilt in CON and SHD. HF and LF/HF increased with tilt in CON, but not in SHD. Peak and mean T-wave amplitudes declined with tilt in CON but not in SHD. In contrast to CON subjects, RRIV and VR failed to change in SHD patients despite increased HR. This suggests preserved tonic but reduced rhythmic autonomic nervous system activity (ANSA) related modulation of HR, and reduced ANSA effects on VR.

Signal synthesis and positive time frequency distributions

A method for obtaining a generalized transfer function (GTF) of a linear time-varying system based on the evolutionary spectral theory is proposed. This GTF can be used to synthesize the signal, and its magnitude squared function results in the signals positive time frequency distribution that satisfies the marginals (i.e., a Cohen-Posch (1995) TFD). The procedure allows any prior estimate of the GTF to be modified such that the resulting posterior GTF is closest in the least square sense to the prior and satisfies the above mentioned properties. Examples are presented to illustrate the performance of the method.

Properties of the Evolutionary Maximum Entropy Spectral Estimator

2. EVOLUTIONARY MAXIMUM ENTROPY ESTIMATION Using maximum entropy spectral analysis and the theThe Wold-Cramer representation [4] of a non-stationary by considering it the output of a linear timevarying system (LTV) with white noise as input: ory of the Wold-Cramer evolutionary spectrum we develop signal is the evolutionary maximum entropy @ME) estimator for non-stationary signals. The EME estimation reduces to the fitting of a time-varying autoregressive model to the Fourier coefficients of the evolutionary spectrum. The model parameters are efficientlv found bv means of the Levinson alH(n, w)ejwndZ(w) (1) gorithm. Just as in the stationary case, the EME estimator provides very good frequency resolution and can be used to obtain autoregressive models. In this paper, we present the EME estimator and discuss some of its properties. Our aim is to show that the EME estimator has analogous properties to the classical ME estimator for stationary signals.

Instantaneous changes in the heart rate variability during head-up tilt revealed by positive time-frequency distribution

Energy distribution of the heart rate variability signal is perturbed in patients with impaired cardiac function compared to normal subjects (Li et al., 1997). We hypothesized that the energy distribution reflects the changes in autonomic regulation that are not exposed by conventional methods estimating the power in the empirically defined frequency ranges. To test this hypothesis instantaneous power changes in the heart rate variability signal were computed between 0.0025 and 0.25 Hz in 20 patients undergoing head-up tilting. Positive time frequency distribution (TFD) was obtained by the method of minimum cross entropy (Loughlin et al., 1994) that satisfies the time and frequency marginals. The distribution of power was calculated by separating the total frequency range into seven scales. Significant changes in the mean spectral power and its distribution were observed in those patients who experienced symptoms compared to those who were asymptomatic. We conclude that the loss of spectral power and changes in the power distribution revealed by positive TFD can be useful for assessment of physiological adaptation and diagnosis of the disorders related to autonomic imbalance.