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Related Concept Videos

Classification of Systems-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
Cyclic Processes And Isolated Systems01:19

Cyclic Processes And Isolated Systems

A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state. 
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Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.

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An Introduction to Processing, Fitting, and Interpreting Transient Absorption Data
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Continuous time modelling with individually varying time intervals for oscillating and non-oscillating processes.

Manuel C Voelkle1, Johan H L Oud

  • 1Max Planck Institute for Human Development, 14195 Berlin, Germany. voelkle@mpib-berlin.mpg.de

The British Journal of Mathematical and Statistical Psychology
|March 17, 2012
PubMed
Summary

Longitudinal studies can effectively use unequal time intervals between assessments. This approach, particularly with continuous time models, offers advantages over strictly equal intervals, especially at low sampling rates.

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Longitudinal Data Analysis

Background:

  • Longitudinal studies often aim for equal time intervals between assessments, but this is rarely achieved in practice.
  • Irregularly spaced assessment waves are common, posing challenges for traditional discrete-time models.
  • Continuous time models in structural equation modeling have been developed to address irregularly spaced data.

Purpose of the Study:

  • To extend continuous time models to accommodate individually varying time intervals for both oscillating and non-oscillating processes.
  • To demonstrate that equal time intervals are not necessary and that unequal sampling intervals can be advantageous, especially at low sampling rates.
  • To highlight the importance of accounting for exact time intervals in longitudinal data analysis.

Main Methods:

  • Application of continuous time models using structural equation modeling.
  • Extension of these models to handle individually varying time intervals.
  • Comparison of continuous time models with varying intervals to standard discrete-time models.
  • Monte Carlo simulation to investigate the effect of different sampling intervals on parameter estimation.

Main Results:

  • Continuous time models effectively handle irregularly spaced longitudinal data.
  • Unequal sampling intervals can be beneficial, particularly when the sampling rate is low.
  • Accounting for exact time intervals is crucial for accurate modeling of longitudinal processes.
  • Varying time intervals did not hinder, and in some cases improved, the estimation of oscillating and non-oscillating processes.

Conclusions:

  • Individually varying time intervals in longitudinal studies should be embraced as an opportunity, not a problem.
  • Researchers are encouraged to utilize continuous time models that accommodate non-uniform time intervals.
  • Accurate modeling of longitudinal data requires careful consideration of the precise timing of assessments.