Howard C. Lee

Comparison of time-frequency distribution techniques for analysis of simulated Doppler ultrasound signals of the femoral artery

The time-frequency distribution of the Doppler ultrasound blood flow signal is normally computed by using the short-time Fourier transform or autoregressive modeling. These two techniques require stationarity of the signal during a finite interval. This requirement imposes some limitations on the distribution estimate. In the present study, three new techniques for nonstationary signal analysis (the Choi-Williams distribution, a reduced interference distribution, and the Bessel distribution) were tested to determine their advantages and limitations for analysis of the Doppler blood flow signal of the femoral artery. For the purpose of comparison, a model simulating the quadrature Doppler signal was developed, and the parameters of each technique were optimized based on the theoretical distribution. Distributions computed using these new techniques were assessed and compared with those computed using the short-time Fourier transform and autoregressive modeling. Three indexes, the correlation coefficient, the integrated squared error, and the normalized root-mean-squared error of the mean frequency waveform, were used to evaluate the performance of each technique. The results showed that the Bessel distribution performed the best, but the Choi-Williams distribution and autoregressive modeling are also techniques which can generate good time-frequency distributions of Doppler signals.<<ETX>>

The time-frequency distributions of nonstationary signals based on a Bessel kernel

A kernel based on the first kind Bessel function of order one is proposed to compute the time-frequency distributions of nonstationary signals. This kernel can suppress the cross terms of the distribution effectively. It is shown that the Bessel distribution (the time-frequency distribution using Bessel kernel) meets most of the desirable properties with high time-frequency resolution. A numerical alias-free implementation of the distribution is presented. Examples of applications in time-frequency analysis of the hearts sound and Doppler blood flow signals are given to show that the Bessel distribution can be easily adapted to two very different signals for cardiovascular signal processing. By controlling a kernel parameter, this distribution can be used to compute the time-frequency representations of transient deterministic and random signals. The study confirms the potentials of the proposed distribution in nonstationary signal analysis. >

Analysis-synthesis of the phonocardiogram based on the matching pursuit method

The matching pursuit method of Mallat and Zhang (1993) is applied to the analysis and synthesis of phonocardiograms (PCGs). The method is based on a classical Gabor wavelet or time-frequency atom which is the product of a sinusoid and a Gaussian window function, it decomposes a signal into a series of time-frequency atoms by an iterative process based on selecting the largest inner product of the signal (and the subsequent residues) with atoms from a redundant dictionary. The Gaussian window controls the envelope duration and time position of each atom; and the sinusoid represents the frequency. The method was applied to two sets of PCGs: one with very low-noise level and the other with 10% noise energy. Each database includes 11 PCGs representing the normal and the pathological conditions of the heart. The normalized root-mean-square error (NRMSE) was computed between the original and the reconstructed signals. The results show that the matching pursuit method is very suitable to the transient and complex properties of the PCGs, as it yielded excellent NRMSEs around 2.2% for the two sets of 11 PCGs tested.

Time-frequency scaling transformation of the phonocardiogram based of the matching pursuit method

A time-frequency scaling transformation based on the matching pursuit (MP) method is developed for the phonocardiogram (PCG). The MP method decomposes a signal into a series of time-frequency atoms by using an iterative process. The modification of the time scale of the PCG can be performed without perceptible change in its spectral characteristics. It is also possible to modify the frequency scale without changing the temporal properties. The technique has been tested on 11 PCGs containing heart sounds and different murmurs. A scaling/inverse-scaling procedure was used for quantitative evaluation of the scaling performance. Both the spectrogram and a MP-based Wigner distribution were used for visual comparison in the time-frequency domain. The results showed that the technique is suitable and effective for the time-frequency scale transformation of both the transient property of the heart sounds and the more complex random property of the murmurs. It is also shown that the effectiveness of the method is strongly related to the optimization of the parameters used for the decomposition of the signals.

Artificial neural networks in computer-assisted classification of heart sounds in patients with porcine bioprosthetic valves.

The paper describes the design, training and testing of a three-layer feedforward back-propagation neural network for the classification of bioprosthetic valve closure sounds. Forty-seven patients with a porcine bioprosthetic valve inserted in the aortic position were involved in the study. Twenty-four of them had a normal bioprosthetic valve, and the other 23 had a degenerated valve. Five features extracted from the Fourier spectra and 12 linear predictive coding (LPC) coefficients of the sounds were used separately as the input of two neural-network classifiers. The performance of the classifiers was tested using the leave-one-out method. Results show that correct classifications were 85 per cent using the spectral features, and 89 per cent using the LPC coefficients. The study confirms the potential of artificial networks for the classification of bioprosthetic valve closure sounds. Clinical use of this method, however, still requires further investigation.

Pole-placement control of voltage-regulated PWM rectifiers through real-time multiprocessing

The voltage-regulated pulse-width-modulated (PWM) rectifier is prone to instability. The system can be stabilized by proportional-plus-integral feedback control, but its transient response is slow. The authors describe results of a study of digital control to improve the system dynamic response by pole placement through state feedback. The control algorithm is implemented for real-time operation by using a custom-designed system of three high-speed microprocessors. Results from an experimental study with a 1 kW hardware laboratory model of the PWM rectifier show that the dynamic response can be significantly improved even when the DC link capacitor is substantially reduced.<<ETX>>

Time-frequency analysis of the first heart sound. Part 1 : Simulation and analysis

The authors propose a simulated first heart sound (S1) signal that can be used as a reference signal to evaluate the accuracy of time-frequency representation techniques for studying multicomponent signals. The composition of this simulated S1 is based on the hypothesis that an S1 recorded on the thorax over the apical area of the heart is composed of constant frequency vibrations from the mitral valve and a frequency modulated vibration from the myocardium. Essentially, the simulated S1 consists of a valvular component and a myocardial component. The valvular component is modelled as two exponentially decaying sinusoids of 50 Hz and 150 Hz and the myocardial component is modelled by a frequency modulated wave between 20 Hz and 100 Hz. The study shows that the simulated S1 has temporal and spectral characteristics similar to S1 recorded in humans and dogs. It also shows that the spectrogram cannot resolve the three components of the simulated S1. It is concluded that it is necessary to search for a better time-frequency representation technique for studying the time-frequency distribution of multicomponent signals such as the simulated S1.

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.

Automatic detection of sounds and murmurs in patients with lonescu-Shiley aortic bioprostheses

The problems encountered in the automatic detection of cardiac sounds and murmurs are numerous. The phonocardiogram (PCG) is a complex signal produced by deterministic events such as the opening and closing of the heart valves, and by random phenomena such as blood-flow turbulence. In addition, background noise and the dependence of the PCG on the recording sites render automatic detection a difficult task. In the paper we present an iterative automatic detection algorithm based on the a priori knowledge of spectral and temporal characteristics of the first and second heart sounds, the valve opening clicks, and the systolic and diastolic murmurs. The algorithm uses estimates of the PCG envelope and noise level to identify iteratively the position and duration of the significant acoustic events contained in the PCG. The results indicate that it is particularly effective in detecting the second heart sound and the aortic component of the second heart sound in patients with lonescu-Shiley aortic valve bioprostheses. It has also some potential for the detection of the first heart sound, the systolic murmur and the diastolic murmur.

Cardiac doppler blood-flow signal analysis

The normality (Gaussian property) and stationarity of the cardiac Doppler blood-flow signal were evaluated on short-time segments distributed over the cardiac cycle. The basic approaches used to perform statistical tests on the nonstationary and quasiperiodic cardiac Doppler signal are presented. The results obtained from the data of ten patients having a normal aortic valve and ten patients having a stenotic valve indicate that a complex Gaussian random process is an acceptable approximation for the clinical cardiac Doppler signal. For segments of 10 ms or less, 82 per cent of them were accepted to be stationary with a significance level of 0.05, whereas for durations greater than 40 ms, the percentage of stationary segments was less than 75 per cent. It was concluded that the 10ms window generally used in practice is a good choice for Doppler spectrogram estimation, but a shorter time interval would be preferable.