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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

341
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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Sampling Theorem01:15

Sampling Theorem

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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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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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Aliasing01:18

Aliasing

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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...
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Sampling Methods: Overview01:06

Sampling Methods: Overview

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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. 
In analytical chemistry, the choice of...
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Sampling Distribution01:12

Sampling Distribution

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Stability of Sampled-Data Systems With Packet Losses: A Nonuniform Sampling Interval Approach.

Wenbing Zhang, Yang Tang, Wei Xing Zheng

    IEEE Transactions on Cybernetics
    |August 17, 2022
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    Summary

    This study introduces a nonuniform sampling interval approach for sampled-data systems, enhancing stability even with packet losses. The method extends the Halanay inequality, reducing conservatism and allowing for more robust stability analysis.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Applied Mathematics

    Background:

    • Stability analysis of sampled-data systems is crucial for reliable control.
    • Existing methods often face conservatism, especially with packet losses and nonuniform sampling.
    • The Halanay inequality provides a foundation for stability analysis but requires adaptation for sampled-data systems.

    Purpose of the Study:

    • To develop a novel approach for analyzing the exponential stability of sampled-data systems with packet losses.
    • To reduce the conservatism associated with existing stability criteria.
    • To extend stability analysis to nonlinear systems with strong nonlinearities.

    Main Methods:

    • Extension of the Halanay inequality to sampled-data systems, incorporating an exponential gain controller.
    • Development of a new lemma to generalize the Halanay-like inequality, accommodating packet losses.
    • Application of the generalized inequality to establish exponential stability conditions for linear and nonlinear systems.

    Main Results:

    • Sufficient conditions for exponential stability of linear sampled-data systems are derived.
    • The maximal allowable sampling interval bound is linked to Halanay inequality's constant terms.
    • A decay rate is expressed using the Lambert W function, and conservatism is reduced compared to Gronwall-Bellman Lemma-based methods.

    Conclusions:

    • The proposed nonuniform sampling interval approach effectively enhances stability for sampled-data systems with packet losses.
    • The generalized Halanay-like inequality allows for stability analysis even when some sampling intervals exceed traditional bounds.
    • The methodology is applicable to nonlinear systems, demonstrating robustness and broader applicability.