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Related Concept Videos

Classification of Systems-II01:31

Classification of Systems-II

175
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,
175
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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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...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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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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Basic Continuous Time Signals01:22

Basic Continuous Time Signals

237
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...
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
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Updated: Jul 19, 2025

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans
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Evaluating Discrete Time Methods for Subgrouping Continuous Processes.

Jonathan J Park1, Zachary F Fisher1, Sy-Miin Chow1

  • 1Department of Human Development and Family Studies, The Pennsylvania State University.

Multivariate Behavioral Research
|August 17, 2023
PubMed
Summary
This summary is machine-generated.

Discrete-time subgrouping methods, like vector autoregression (VAR), effectively identify human process dynamics when data measurement intervals capture system behavior. This research clarifies their utility for continuous-time data analysis.

Keywords:
Dynamic network modelingcontinuous-timevector autoregression

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Area of Science:

  • Psychometrics
  • Computational Social Science
  • Time Series Analysis

Background:

  • Human process modeling increasingly focuses on time scales and heterogeneity.
  • Discrete-time subgrouping methods, such as vector autoregression (VAR), are used to find shared trends in individual data.
  • The accuracy of VAR parameters depends on data measurement intervals.

Purpose of the Study:

  • To evaluate the strengths and limitations of discrete-time subgrouping methods in recovering subgroup dynamics under varying measurement intervals.
  • To clarify the implications of using discrete-time methods (scgVAR, S-GIMME) on continuous-time data.

Main Methods:

  • Monte Carlo simulation study.
  • Application of discrete-time subgrouping methods (subgrouped chain graphical VAR, S-GIMME) to continuous-time data.
  • Analysis of subgroup recovery under different measurement intervals.

Main Results:

  • Discrete-time subgrouping methods successfully recover true subgroups when measurement intervals are sufficiently large.
  • Adequate intervals capture the system's dynamics through lagged or contemporaneous effects.
  • Performance is contingent on the relationship between measurement interval and system dynamics.

Conclusions:

  • Discrete-time subgrouping methods can be reliable for analyzing continuous-time data if measurement intervals are appropriately chosen.
  • Understanding the interplay between measurement intervals and system dynamics is crucial for accurate subgroup identification.
  • Further research is needed to explore the limitations and implications in diverse modeling contexts.