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Related Concept Videos

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

264
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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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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Linear time-invariant Systems01:23

Linear time-invariant Systems

319
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...
319
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence...
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Reversible and Irreversible Processes01:14

Reversible and Irreversible Processes

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The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
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Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
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Explicitly Solvable Continuous-time Inference for Partially Observed Markov Processes.

Daniel Chen, Alexander G Strang, Andrew W Eckford

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    |January 30, 2023
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    This study introduces a continuous-time sum-product algorithm for inferring hidden states in Markov processes from partial observations. The new method accurately calculates conditional probabilities, demonstrated using a cystic fibrosis transmembrane conductance regulator (CFTR) model.

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    Area of Science:

    • Computational Biology
    • Statistical Modeling
    • Biophysics

    Background:

    • Many systems are modeled as discrete state Markov processes with partially observable states.
    • Inferring hidden states from partial observations is crucial for understanding system dynamics.
    • Existing methods often rely on discrete-time observations, limiting applicability.

    Conclusions:

    • The continuous-time sum-product algorithm provides a powerful tool for state inference in dynamic systems.
    • This method offers precise conditional probability calculations, enhancing the analysis of partially observed processes.
    • The CFTR protein application highlights the algorithm's potential in biological and biophysical research.