Shlomo Engelberg

Limitations of the describing function for limit cycle prediction

We consider comparator-based nonlinear feedback systems, and use Tsypkins method to develop a strategy with which to find systems with low-pass linear part for which the describing function technique erroneously predicts limit cycles. We produce an infinite set of examples of systems with very low-pass linear parts for which the describing function technique predicts spurious limit cycles, and also provide a more practical example in which limit cycles are erroneously predicted.

Formation of singularities in the Euler and Euler-Poisson equations

Abstract We establish finite-time loss of smoothness for several variants of the one-dimensional Euler equations. We consider the Euler-Poisson equations in one dimension and the Euler and Euler-Poisson equations in three dimensions in the presence of spherical or cylindrical symmetry. We show that no matter how smooth the initial data are, solutions of these equations can be forced to lose smoothness in finite-time. By using an interesting variant of Laxs method for showing the finite-time loss of smoothness of solutions of pairs of hyperbolic conservation laws, we show the finite-time loss of smoothness of solutions of the one-dimensional Euler-Poisson equations. Using our method, we also find a sufficient condition for the existence of a globally smooth solution of the one-dimensional Euler-Poisson equations. For the other cases, we use a characteristic-based method. In all cases, we give local conditions for the finite-time loss of smoothness of solutions.

Three-wavelength technique for the measurement of oxygen saturation in arterial blood and in venous blood

Pulse oximetry is an optical technique for the assessment of oxygen saturation in arterial blood and is based on the different light absorption spectra for oxygenated and deoxygenated hemoglobin and on two-wavelength photoplethysmographic (PPG) measurement of arterial blood volume increase during systole. The technique requires experimental calibration for the determination of the relationship between PPG-derived parameters and arterial oxygen saturation, and this calibration is a source of error in the method. We suggest a three-wavelength PPG technique for the measurement of arterial oxygen saturation that has no need for calibration if the three wavelengths are properly selected in the near-infrared region. The suggested technique can also be implemented for the assessment of venous oxygen saturation by measuring the decrease in transmission of light through a tissue after increasing its blood volume by venous occlusion. The oxygen saturation in venous blood is a parameter that is related to oxygen consumption in tissue and to tissue blood flow. The three-wavelength method has the potential to provide accurate oxygen saturation measurements in arterial and venous blood, but experimental validation of the theory is still required to confirm this claim.

A Comment on the Karpovsky–Taubin Code

This paper presents generalizations of the Karpovsky-Taubin nonlinear code. The generalizations lead to robust and partially robust single error detecting codes and single error correcting codes.

Calibration-Free Pulse Oximetry Based on Two Wavelengths in the Infrared — A Preliminary Study

The assessment of oxygen saturation in arterial blood by pulse oximetry (SpO2) is based on the different light absorption spectra for oxygenated and deoxygenated hemoglobin and the analysis of photoplethysmographic (PPG) signals acquired at two wavelengths. Commercial pulse oximeters use two wavelengths in the red and infrared regions which have different pathlengths and the relationship between the PPG-derived parameters and oxygen saturation in arterial blood is determined by means of an empirical calibration. This calibration results in an inherent error, and pulse oximetry thus has an error of about 4%, which is too high for some clinical problems. We present calibration-free pulse oximetry for measurement of SpO2, based on PPG pulses of two nearby wavelengths in the infrared. By neglecting the difference between the path-lengths of the two nearby wavelengths, SpO2 can be derived from the PPG parameters with no need for calibration. In the current study we used three laser diodes of wavelengths 780, 785 and 808 nm, with narrow spectral line-width. SaO2 was calculated by using each pair of PPG signals selected from the three wavelengths. In measurements on healthy subjects, SpO2 values, obtained by the 780–808 nm wavelength pair were found to be in the normal range. The measurement of SpO2 by two nearby wavelengths in the infrared with narrow line-width enables the assessment of SpO2 without calibration.

A note on conjugate gradient convergence – Part II

Summary. Continuing our previous analysis, we derive the exact number of conjugate gradient iterations needed (to achieve a given tolerance) for the one-dimensional discrete Poisson equation on a uniform grid, and a particularly smooth solution vector.

An analytical proof of the linear stability of the viscous shock profile of the burgers equation with fourth-order viscosity

In this paper we establish the exponential decay of solutions of the equation u_t + \varphi(x) u_x = - \partial_x^4 u in an exponentially weighted norm. Here

Comparison of Systolic Blood Pressure Values Obtained by Photoplethysmography and by Korotkoff Sounds

\varphi(x)

The stability of the viscous shock profiles of the burgers’ equation with a fourth order viscosity

is the viscous shock profile corresponding to the Burgers equation with fourth-order viscosity: u_t + u u_x = - \partial_x^4 u. Because of the fact that the profile is not monotone, showing the stability is nontrivial. We extend the techniques of Koppel and Howard, (Adv. Math. 18 (1975), pp. 306-358), techniques that they employ to prove the existence of the viscous shock profile, and we use the techniques to prove the stability of the viscous shock profile. We have previously shown that the viscous shock profile is a stable solution in an exponentially weighted norm by making use of numerical results. The main advantage of our current method is that it is analytical. One sees more clearly what properties of the viscous shock profile cause it to be a stable solution of the PDE.

Precise variable-Q filter design [DSP Tips & Tricks]

In the current study, a non-invasive technique for systolic blood pressure (SBP) measurement based on the detection of photoplethysmographic (PPG) pulses during pressure-cuff deflation was compared to sphygmomanometry—the Korotkoff sounds technique. The PPG pulses disappear for cuff-pressures above the SBP value and reappear when the cuff-pressure decreases below the SBP value. One hundred and twenty examinations were performed on forty subjects. In 97 examinations the two methods differed by less than 3 mmHg. In nine examinations the SBP value measured by PPG was higher than that measured by sphygmomanometry by 5 mmHg or more. In only one examination the former was lower by 5 mmHg or more than the latter. The appearance of either the PPG pulses or the Korotkoff sounds assures that the artery under the cuff is open during systolic peak pressure. In the nine examinations mentioned above the PPG pulses were observed while Korotkoff sounds were not detected, despite the open artery during systole. In these examinations, the PPG-based technique was more reliable than sphygmomanometry. The high signal-to-noise ratio of measured PPG pulses indicates that automatic measurement of the SBP by means of automatic detection of the PPG signals is feasible.