Stray free switched capacitor loop biquad that realizes different generic transfer functions

Peripheral exercise blood pressure and resting central blood pressure are considered more relevant to cardiovascular health than resting peripheral blood pressure. Central exercise blood pressure may well be an even more useful measure, but there is no simple non-invasive means of determining it. The aim of the present study was to establish whether the estimation of central blood pressure from peripheral blood pressure using a transfer function derived at rest, would hold after aerobic exercise. Thirty healthy young men were studied before and immediately (< 1 min) and 10 min after 15 min bicycle exercise at 65-70% of maximum heart rate. Simultaneous carotid and radial artery waveforms were recorded, and radial-to-carotid generalized transfer functions (GTF) were calculated using Fourier analysis for rest and immediately postexercise. Central systolic blood pressure (SBP) and augmentation index (AIx) were calculated for measured and derived waves. The resting GTF underestimated central SBP and AIx immediately (-5.8 +/- 2.1 mmHg, P = 0.01; -8.3 +/- 2.9%, P = 0.008) and 10 min after (-2.0 +/- 0.7 mmHg, P = 0.008; -7.0 +/- 2.1%, P = 0.003) exercise. No significant bias was found between measured and derived (using resting GTF) carotid values at rest. The use of an exercise-specific GTF resulted in no specific bias immediately or 10 min after exercise, although it overestimated blood pressure and AIx at rest (2.5 +/- 1.0 mmHg, P = 0.02; 11.3 +/- 3.0%, P = 0.001). A peripheral-to-central arterial GTF derived at rest significantly underestimates key measures of central arterial pressure immediately after exercise, and pressure estimations may be improved by the use of an exercise-specific GTF.

In this paper the problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type that converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second-order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions. Two numerical examples demonstrate the effectiveness of the algorithm.

Introduction: Central aortic pressure waveform analyses can provide clinically relevant information beyond conventional brachial blood pressure (BP) assessment. This waveform can be reproduced noninvasively through application of a generalized transfer function (GTF) on a peripheral waveform, as conventionally performed by applanation tonometry. Photoplethysmography (PPG) is an alternate approach; however, differences in measurement site and modality demand the use of a transfer function (TF) specific for those differences. This study aimed to compare central aortic waveform features generated from radial tonometry (reference) using a proprietary GTF with a central aortic waveform and its features generated from a simultaneous fingertip PPG measurement using a selective method where one of three different TFs is chosen based on the input signal harmonic profile. Methods: Brachial BP was measured in triplicate under resting conditions and was used for subsequent calibration. Multiple simultaneous radial tonometry (SphygmoCor CVMS) and fingertip PPG measurements were then performed in individual participants (n = 21, 10 females, age: 39 ± 16 years). Measurements were converted into central aortic waveforms with their respective TFs. Twenty central aortic pressure waveform parameters were compared through correlation analysis, Bland-Altman plots, and a repeated measure mixed-effects ANOVA model. Central aortic waveform shape was compared using the root-mean-squared error (RMSE). Results: Correlation (r) of PPG-derived parameters with radially tonometry-derived central aortic parameters was high ranging from 0.79 to 0.99. Mean differences of pressure-related parameters were within 1.3 mm Hg, and differences of time-related parameters ranged from −2.2 to 3.4%. While some parameters were statistically different, these differences are not physiologically meaningful. Central aortic waveform shape had an average RMSE of 1.8 ± 0.9%. Conclusion: Fingertip PPG-derived central aortic waveform parameters using a novel selective TF were comparable to central aortic waveform features derived from radial tonometry using a previously validated GTF.

This paper studies the generation of stable transfer functions for which the real or imaginary part takes prescribed values at discrete uniformly spaced points on the unit circle. Formulas bounding the error between a particular interpolating function and any function consistent with the data are presented, which have the desirable property that the error goes to zero exponentially fast with the number of interpolating points. The paper also examines generation of stable minimum phase transfer functions for which the magnitude takes prescribed values at uniformly spaced points on the unit circle, and presents error bounds for this problem. Connection with the discrete Hilbert transform is made. The effect of uncertainty in the original data is also examined.

This study describes the use of a biofeedback method for the noninvasive study of baroreflex mechanisms. Five previously untrained healthy male participants learned to control oscillations in heart rate using biofeedback training to modify their heart rate variability at specific frequencies. They were instructed to match computer-generated sinusoidal oscillations with oscillations in heart rate at seven frequencies within the range of 0.01-0.14 Hz. All participants successfully produced high-amplitude target-frequency oscillations in both heart rate and blood pressure. Stable and predictable transfer functions between heart rate and blood pressure were obtained in all participants. The highest oscillation amplitudes were produced in the range of 0.055-0.11 Hz for heart rate and 0.02-0.055 Hz for blood pressure. Transfer functions were calculated among sinusoidal oscillations in the target stimuli, heart rate, blood pressure, and respiration for frequencies at which subjects received training. High and low target-frequency oscillation amplitudes at specific frequencies could be explained by resonance among various oscillatory processes in the cardiovascular system. The exact resonant frequencies differed among individuals. Changes in heart rate oscillations could not be completely explained by changes in breathing. The biofeedback method also allowed us to quantity characteristics of inertia, delay, and speed sensitivity in baroreflex system. We discuss the implications of these findings for using heart rate variability biofeedback as an aid in diagnosing various autonomic and cardiovascular system disorders and as a method for treating these disorders.

It is shown that a p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sup> m transfer function G(s) with p⩾m can be decomposed as G = (I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ...(I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r+2</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r+2</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> (I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r=1</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r=1</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</sub> where Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> are stable all-pass transfer functions, 1=ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ..=ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ≫ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r=1</sub> ..≫ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> ≫0 are the Hankel-singular-values of GW* <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> where G*G=WW* with W stable and minimum phase. Results on the McMillan degree of G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Λ</sup> :=(I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> )..(I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> )G then show that G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Λ</sup> gives a good low order approximation to G in the sense of relative error.

Conditions for a Class of Rational Approximants of Fractional Differentiators/Integrators to Enjoy the Interlacing Property

A new method-based on transformations from 1-variable transfer functions is presented for the design of stable 2-variable transfer functions. As compared with already existing methods, this method results in a good response obtained through fewer numbers of iterations. The designed filters are always stable without the need of any constraints during minimization.

Gravity is a major recovery mechanism of naturally fractured reservoirs, where fracture gas drains matrix oil until equilibrium is reached with the capillary forces (wrt fluid densities, matrix gas capillary pressure and block height). The challenge of modelling gravity drainage in dual-medium simulation is to match the final maximum recovery, using integrated pseudo-capillary pressure curve, and the correct recovery kinetics. The paper suggests an approach to improve the simulation of the recovery kinetics in gravity drainage by dividing the matrix block for the fluid transfer function in two specific parts: saturation front part (SFP) and initial state part (ISP). As the invading gas enters the matrix the SFP and ISP areas increase and decrease respectively, until the final recovery is reached at equilibrium point. The contributions from each part are summed up to equal a mass conservation equation at each time step for each matrix cell. Properties of SFP depend on the invading fluid saturation and ISP hold the initial state properties, hence its name. This SubFace formulation can be implemented in flow simulator for reservoirs exhibiting a dual-medium behaviour. Our SubFace Transfer Function approach (SF), performs well versus not only conventional transfer functions (Kazemi, Gilman), but also versus two improved ones: Quandalle-Sabathier, and Lu-Blunt (non-Warren-Root General Transfer Function) in matching the results of fine-grid single-medium models under various parameters (capillary pressure, matrix shape and mobility). We also tested SF in mixed-wet water-oil system to assess its capability of modelling gravity and capillary imbibition. This new formulation improves dual-medium simulations of fractured reservoirs with an accurate representation of matrix-fracture exchanges, and better reserves assessment and reservoir management.

BackgroundTo examine whether augmentation index (AIx) is increased in Marfan syndrome (MFS) and associated with increased aortic root size, and whether a peripheral-to-central generalised transfer function (GTF) can be applied usefully in MFS.Methods10 MFS patients and 10 healthy controls (matched for sex, age and height) were studied before and after 400 μg sub-lingual GTN. Arterial waveforms were recorded using applanation tonometry. AIx and pulse pressure (PP) were determined for the radial and carotid arteries. Pulse wave velocity (PWV) was measured between carotid and femoral arteries. GTFs were generated to examine the relationship between radial and carotid waveforms.ResultsAIx was greater in MFS compared to controls at radial (mean -31.4 (SD 14.3)% v -50.2(15.6)%, p = 0.003) and carotid (-7.6(11.2)% v -23.7(12.7)%, p = 0.004) sites. Baseline PP at all measurement sites, and PWV, did not differ between subject groups. Multivariate analysis demonstrated that PWV and carotid AIx were positively correlated with aortic root size (p < 0.001 and p = 0.012 respectively), independent of the presence of MFS. PP was not associated with aortic root size. GTN caused similar decreases in AIx in both controls and patients. Significant differences were found in GTFs between MFS and control subjects, which changed following GTN administration. However, when an independent GTF was used to derive carotid waves from radial waves, no differences were found in the degree of error between MFS and controls.ConclusionAIx is sensitive to the vascular abnormalities present in MFS, and may have a role as an adjunct to measurement of central PP and PWV. Differences between MFS and controls in the nature of the peripheral-to-central GTF are present, although have little effect on the pulse contour.

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 signal's 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.

We study the class of linear differential-algebraic m-input m-output systems which have a transfer function with proper inverse. A sufficient condition for the transfer function to have proper inverse is that the system has ‘strict and non-positive relative degree’. We present two main results: first, a so-called ‘zero dynamics form’ is derived; this form is—within the class of system equivalence—a simple form of the DAE; it is a counterpart to the well-known Byrnes–Isidori form for ODE systems with strictly proper transfer function. The ‘zero dynamics form’ is exploited to characterize structural properties such as asymptotically stable zero dynamics, minimum phase, and high-gain stabilizability. The zero dynamics are characterized by (A, E, B)-invariant subspaces. Secondly, it is shown that the ‘funnel controller’ (that is a static non-linear output error feedback) achieves, for all DAE systems with asymptotically stable zero dynamics and transfer function with proper inverse, tracking of a reference signal by the output signal within a pre-specified funnel. This funnel determines the transient behaviour.

This paper describes a simple procedure for synthesizing an active distributed RC network which, by using dominant poles and zeros, realizes a very accurate approximation of an arbitrary stable rational transfer function. The network uses a single uniformly distributed RC line with taps spaced along its length. A linear combination of tap voltages is added to the input signal to form the driving voltage for the RC line; the output signal is also a linear combination of the tap voltages. The network offers a number of significant advantages. Since it realizes a nearly rational transfer function, the approximation problem can be conveniently solved using readily available results on rational function approximation. Also, the network uses only one uniform RC line, the transfer function can be changed simply by changing resistor values, and the frequency can be scaled by minor connection changes. Thus one standard network with minor modification is useful for a wide variety of applications. This paper develops the design procedure and derives the various sensitivity functions of importance. Two example designs are carried out: an approximation to a second-order low-pass transfer function and an approximation to a second-order band-pass transfer function with a Q of 100. The sensitivities for the examples are very reasonable and the measurements made on laboratory models indicate excellent agreement with theoretical predictions.

In this paper, we discuss the extension of carrier-assisted differential detection (CADD) from using a conventional interferometer to broad ranges of transfer functions. We show that by using a transfer function based on micro-ring resonator, the receiver sensitivity of CADD can be greatly improved.

High‐intensity interval exercise (HIIE) is recommended because it provides favourable haemodynamic stimulation, but excessive haemodynamic fluctuations may be an adverse impact on the brain. We tested whether the cerebral vasculature is protected against systemic blood flow fluctuation during HIIE. Fourteen healthy men (age 24 ± 2 years) underwent four 4‐min exercises at 80–90% of maximal workload (Wmax) interspaced by 3‐min active rest at 50–60% Wmax. Transcranial Doppler measured middle cerebral artery blood velocity (CBV). Systemic haemodynamics (Modelflow) and aortic pressure (AoP, general transfer function) were estimated from an invasively recorded brachial arterial pressure waveform. Using transfer function analysis, gain and phase between AoP and CBV (0.39–10.0 Hz) were calculated. Stroke volume, aortic pulse pressure and pulsatile CBV increased during exercise (time effect: P < 0.0001 for all), but a time‐domain index of aortic–cerebral pulsatile transition (pulsatile CBV/pulsatile AoP) decreased throughout the exercise bouts (time effect: P < 0.0001). Furthermore, transfer function gain reduced, and phase increased throughout the exercise bouts (time effect: P < 0.0001 for both), suggesting the attenuation and delay of pulsatile transition. The cerebral vascular conductance index (mean CBV/mean arterial pressure; time effect: P = 0.296), an inverse index of cerebral vascular tone, did not change even though systemic vascular conductance increased during exercise (time effect: P < 0.0001). The arterial system to the cerebral vasculature may attenuate pulsatile transition during HIIE as a defence mechanism against pulsatile fluctuation for the cerebral vasculature.