Fractional Differential Equations

Problem Given the number of times in which an unknown event has happened and failed: Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named. SECTION 1 Definition 1. Several events are inconsistent, when if one of them happens, none of the rest can. 2. Two events are contrary when one, or other of them must; and both together cannot happen. 3. An event is said to fail, when it cannot happen; or, which comes to the same thing, when its contrary has happened. 4. An event is said to be determined when it has either happened or failed. 5. The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon it’s 2 happening.

An essay towards solving a problem in the doctrine of chances. [Facsimil]

Fundamentals of statistical signal processing: Estimation theory: by Steven M. KAY; Prentice Hall signal processing series; Prentice Hall; Englewood Cliffs, NJ, USA; 1993; xii + 595 pp.; $65; ISBN: 0-13-345711-7

Digital control system analysis and design

The use of automated blood pressure (BP) monitoring is growing as it does not require much expertise and can be performed by patients several times a day at home. Oscillometry is one of the most common measurement methods used in automated BP monitors. A review of the literature shows that a large variety of oscillometric algorithms have been developed for accurate estimation of BP but these algorithms are scattered in many different publications or patents. Moreover, considering that oscillometric devices dominate the home BP monitoring market, little effort has been made to survey the underlying algorithms that are used to estimate BP. In this review, a comprehensive survey of the existing oscillometric BP estimation algorithms is presented. The survey covers a broad spectrum of algorithms including the conventional maximum amplitude and derivative oscillometry as well as the recently proposed learning algorithms, model-based algorithms, and algorithms that are based on analysis of pulse morphology and pulse transit time. The aim is to classify the diverse underlying algorithms, describe each algorithm briefly, and discuss their advantages and disadvantages. This paper will also review the artifact removal techniques in oscillometry and the current standards for the automated BP monitors.

Oscillometric Blood Pressure Estimation: Past, Present, and Future

The problem of detecting a periodic signal buried in zero-mean Gaussian noise is present in various fields of engineering. It is well-known that the amplitude of the disturbed signal follows a Rice distribution which is characterized by two parameters. In this paper, an alternative Bayesian approach is proposed to tackle this two-parameter estimation problem. By incorporating prior knowledge into a mathematical framework, the drawbacks of the existing methods (i.e., the maximum likelihood approach and the method of moments) can be overcome. The performance of the proposed Bayesian estimatoris shown through simulations.

Estimating the parameters of a Rice distribution: A Bayesian approach

Measuring the blood pressure as accurately as possible can save a lot of human lives. Hence, it is very important to find an optimal method to determine the systolic and diastolic pressures out of the measured oscillometric blood pressure waveform (OBPW). Recently, studies have shown that by working in the frequency domain, outperforming results could be obtained for the separation of breathing from cardiac activity. In this paper, we present a new implementation of the Kalman filtering algorithm to estimate the envelope of the cardiac activity. Even though the alternating Kalman filter algorithm has subharmonic infiltrations, it offers an envelope that, when applied together with the Windkessel model for calibration, substantially reduces the error of the calibrated systolic and diastolic pressures. This important result validates the non-linear model for the OBPW, as well as the Windkessel model for calibration.

Using Alternating Kalman Filtering to Analyze Oscillometric Blood Pressure Waveforms

A method to characterize the memory effects in a nonlinear concurrent dual-band transmitter is presented. It is an extension of the conventional two-tone test for power amplifiers to concurrent dual-band transmitters. The output signal of a concurrent dual-band transmitter is affected not only by intermodulation (IM) products but also by cross-modulation (CM) products. In one frequency band, the transmitter is excited by a two-tone signal which frequency separation is swept. In the second band, the transmitter is concurrently excited by another two-tone signal with slightly wider frequency separation. The frequency difference of the two signals is fixed during the frequency sweep. The two-tone test is made at different power levels. The upper and lower third-order IM and CM products are measured. The asymmetry between the upper and lower third-order IM and CM products are measures of the transmitter’s memory effects. The measurement results show that the memory effects are more dominant in the third-order IM products than in the CM products. An error analysis and system calibration was performed and measurement results for two different devices are presented.

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Characterization of Concurrent Dual-Band Power Amplifiers Using a Dual Two-Tone Excitation Signal

Proving the Usefulness of a 3-port Nonlinear Vectorial Network Analyser through Mixer Measurements

Unlike the Vectorial Network Analyser, the Nonlinear Vectorial Network Analyser imposes a wideband intermediate frequency (IF) detection (a few kHz instead of Hz). In this paper, the influence of the resulting signal-to-noise degradation on the calibration accuracy is analysed. The statistical properties of a standard calibration are compared to a stochastically founded method based on real experimental data.

Wendy Van Moer

Papers

Estimating the parameters of a Rice distribution: A Bayesian approach

Using Alternating Kalman Filtering to Analyze Oscillometric Blood Pressure Waveforms

Characterization of Concurrent Dual-Band Power Amplifiers Using a Dual Two-Tone Excitation Signal

Proving the Usefulness of a 3-port Nonlinear Vectorial Network Analyser through Mixer Measurements

Calibration of a Wideband IF Nonlinear Vectorial Network Analyser