A uniqueness problem for the envelope of an oscillatory process

1979 ◽  
Vol 16 (4) ◽  
pp. 822-829 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Stochastic Processes ◽  
Stationary Process ◽  
Transient Processes ◽  
Uniqueness Problem ◽  
Oscillatory Process ◽  
Linear Filter ◽  
Time Varying ◽  
Definition Of ◽  
Oscillatory Processes

In a previous paper, the author has described a method for obtaining envelope processes for oscillatory stochastic processes. These are processes which can be represented as the output of a time-varying linear filter whose input is a stationary process.It is shown in this paper that the proposed definition of the envelope process may not be unique, but may depend on the particular representation of the oscillatory process chosen.It is then shown that for a class of oscillatory processes which is of particular interest, the class of transient processes, there is a class of natural representations which all lead to a unique envelope process.

A uniqueness problem for the envelope of an oscillatory process

1979 ◽  
Vol 16 (04) ◽  
pp. 822-829
Author(s):  
A. M. Hasofer
Keyword(s):  
Stochastic Processes ◽  
Stationary Process ◽  
Transient Processes ◽  
Uniqueness Problem ◽  
Oscillatory Process ◽  
Linear Filter ◽  
Time Varying ◽  
Definition Of ◽  
Oscillatory Processes

In a previous paper, the author has described a method for obtaining envelope processes for oscillatory stochastic processes. These are processes which can be represented as the output of a time-varying linear filter whose input is a stationary process. It is shown in this paper that the proposed definition of the envelope process may not be unique, but may depend on the particular representation of the oscillatory process chosen. It is then shown that for a class of oscillatory processes which is of particular interest, the class of transient processes, there is a class of natural representations which all lead to a unique envelope process.

scholarly journals G-Filtering Nonstationary Time Series

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Mengyuan Xu ◽  
Krista B. Cohlmia ◽  
Wayne A. Woodward ◽  
Henry L. Gray
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Nonstationary Time Series ◽  
Linear Filter ◽  
Time Varying ◽  
Linear Filtering ◽  
Original Process ◽  
Filtering Method ◽  
Time Deformation ◽  
Time Varying Frequency

The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series, the TVF components often overlap in time. In such a situation, the classical linear filtering method fails to extract components from the original process. In this paper, we introduce and theoretically develop the G-filter based on a time-deformation technique. Simulation examples and a real bat echolocation example illustrate that the G-filter can successfully filter a G-stationary process whose TVF components overlap with time.

Epidemic-Like Stochastic Processes with Time-Varying Behavior

2018 ◽  
Vol 45 (3) ◽  
pp. 160-166
Author(s):  
Yingdong Lu ◽  
Mark S. Squillante ◽  
Chai Wah Wu
Keyword(s):  
Stochastic Processes ◽  
Time Varying

Properties and applications of stochastic processes with stationarynth-order increments

1974 ◽  
Vol 6 (3) ◽  
pp. 512-523 ◽  
Author(s):  
B. Picinbono
Keyword(s):  
Stochastic Processes ◽  
Stationary Process ◽  
General Description ◽  
Linear Filtering ◽  
Stationary Increments ◽  
Physical Problems

Many physical problems are described by stochastic processes with stationary increments. We present a general description of such processes. In particular we give an expression of a process in terms of its increments and we show that there are two classes of processes: diffusion and asymptotically stationary. Moreover, we show that thenth increments are given by a linear filtering of an arbitrary stationary process.

Simulation of oscillatory processes in the MVSTUDIUM package

2022 ◽  
Vol 14 (4) ◽  
pp. 139-148
Author(s):  
Aleksandr Poluektov ◽  
Konstantin Zolnikov ◽  
V. Antsiferova
Keyword(s):  
Mathematical Model ◽  
Friction Force ◽  
Computer Models ◽  
3D Models ◽  
Oscillatory Process ◽  
Suspension Point ◽  
Factors Affecting ◽  
2D And 3D ◽  
The Mathematical Model ◽  
Oscillatory Processes

The mathematical model and algorithms of oscillatory movements are considered. Various factors affecting the oscillatory process are considered. Oscillatory movements are constructed in the MVSTUDIUM modeling environment. The schemes of three computer models demonstrating oscillatory processes are determined: a model of a pendulum with a non-movable suspension point, a model of a pushing pendulum with friction force and a model of a breaking pendulum. Classes are being built to execute models with embedded properties, as well as with the ability to export the created classes to other models, and embed classes created by the program developer into the model. Creation of 2D and 3D models of oscillatory processes, an experiment behavior map and a virtual stand.

Some comments on spectral representations of non-stationary stochastic processes

1973 ◽  
Vol 10 (04) ◽  
pp. 881-885 ◽  
Author(s):  
H. Tong
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Stationary Stochastic Process ◽  
Sufficient Condition ◽  
Stationary Stochastic Processes ◽  
Spectral Representations ◽  
Oscillatory Processes

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.

Description of LV pressure-volume relations by time-varying elastance and source resistance

1987 ◽  
Vol 253 (1) ◽  
pp. H83-H90 ◽  
Author(s):  
W. C. Little ◽  
G. L. Freeman
Keyword(s):  
Left Ventricle ◽  
Balloon Occlusion ◽  
Ascending Aorta ◽  
Aortic Flow ◽  
Three Dimensions ◽  
Time Varying ◽  
Source Resistance ◽  
Lv Volume ◽  
Definition Of ◽  
Inotropic Stimulation

If the left ventricle (LV) behaves as a time-varying elastance [E(t)] that is independent of load, then definition of E(t) during normal ejecting beats should permit accurate prediction of LV pressure (LVP) during a maximally afterloaded (isovolumic) beat. We tested this hypothesis in six dogs preinstrumented to measure LVP and aortic flow (Q) and to determine LV volume (V) from three dimensions. LVP and V were varied by caval occlusions. These data were used to determine E(t) and minimal volume required to generate pressure (Vo) at 10-ms intervals during systole using a simple E(t) model, P(t) = E(t) [V(t)-Vo], where P(t) is LVP at any time after the onset of contraction, and V(t) is the LV volume at t. LVP was measured during isovolumic beats generated by sudden balloon occlusion of the ascending aorta. The simple E(t) model accurately predicted isovolumic LVP during the first 70 ms of systole (r = 0.99) and also the end-systolic LVP but underestimated LVP during midsystole by 48 +/- 5 (SD) mmHg (P less than 0.05). When a pressure-dependent source resistance (K = 0.0015 s/ml) was added to the model to reduce LVP in proportion to Q, such that P(t) = E(t) [V(t)-Vo] X [1 - KQ]), LVP during the isovolumic beat was accurately predicted throughout systole (r = 0.99). However, the time to develop peak isovolumic pressure was 22 +/- 7 ms less than predicted. Similar results were obtained during inotropic stimulation with dobutamine in five animals.

QUANTUM ANALYSIS OF OSCILLATORY PROCESSES IN FRACTAL MEDIA

2008 ◽  
Vol 22 (22) ◽  
pp. 3923-3929 ◽  
Author(s):  
F. G. GARASCHENKO ◽  
D. S. KRUCHININ ◽  
V. E. NOVIKOV
Keyword(s):  
Mathematical Models ◽  
Homogeneous Medium ◽  
Oscillatory Process ◽  
Similarity Parameter ◽  
Equivalent Damping ◽  
Quantum Analysis ◽  
Fractal Media ◽  
Fractal Medium ◽  
Oscillatory Processes

On the basis of quantum analysis, we consider the mathematical models applied to the processes of transfer and oscillations in fractal media. It is shown that the equation of oscillations in fractal media with the use of Jackson q-derivatives is similar to that of the oscillatory process in a homogeneous medium with damping. The connection between the similarity parameter of a fractal medium and the equivalent damping is determined. A generalization of the Ohm law for fractal media is obtained.

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