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Related Concept Videos

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.
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Sampling Theorem01:15

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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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BIBO stability of continuous and discrete -time systems01:24

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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.
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Sampling Methods: Overview01:06

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
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Upsampling01:22

Upsampling

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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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Sampling Plans01:23

Sampling Plans

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
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Sampled-Data Stabilization for Boolean Control Networks With Infinite Stochastic Sampling.

Liqing Wang, Zheng-Guang Wu, Shiming Chen

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    Summary
    This summary is machine-generated.

    This study introduces stochastic sampled-data state feedback control for Boolean control networks (BCNs). It provides methods to stabilize BCNs, even with random sampling periods, ensuring system reliability.

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    Area of Science:

    • Control Theory
    • Discrete Systems
    • Stochastic Processes

    Background:

    • Boolean control networks (BCNs) are widely used to model complex systems.
    • Traditional control methods often assume fixed sampling periods, which may not reflect real-world scenarios.
    • Stochastic variations in sampling periods can significantly impact system stability and performance.

    Purpose of the Study:

    • To investigate sampled-data state feedback control for Boolean control networks (BCNs) with stochastic sampling periods.
    • To develop control strategies ensuring stabilization to a fixed point or a specified set.
    • To analyze the impact of different stochastic sampling period distributions on system stability.

    Main Methods:

    • Utilized the algebraic form of BCNs to design stochastic sampled-data state feedback controllers.
    • Considered two distributions for stochastic sampling periods: independent identically distributed (i.i.d.) and infinite Markov processes.
    • Established the equivalence between BCNs with infinite stochastic sampling periods and finite stochastic switched systems.

    Main Results:

    • Derived necessary and sufficient conditions for stabilization and set stabilization of BCNs under stochastic sampling periods.
    • Developed two algorithms for systems with i.i.d. sampling periods.
    • Presented conditions for Markovian sampling periods in a linear programming form, demonstrating effectiveness with examples.

    Conclusions:

    • The proposed stochastic sampled-data state feedback control effectively stabilizes BCNs despite random sampling periods.
    • The study provides a robust framework for analyzing and controlling BCNs with time-varying, stochastic sampling.
    • The results offer practical methods for ensuring system stability in uncertain operational environments.