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相关概念视频

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

251
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...
251
Sampling Theorem01:15

Sampling Theorem

340
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.
340
State Space Representation01:27

State Space Representation

208
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
208
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

204
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
204
Upsampling01:22

Upsampling

237
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...
237
Transfer Function to State Space01:23

Transfer Function to State Space

259
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
259

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A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
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对LSTM的样本数据状态估计

Yongsik Jin, S M Lee

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    此摘要是机器生成的。

    本研究提出了一种新型状态估计器,用于连续长期短期记忆 (LSTM) 神经网络,采用不规则的数据采样. 该方法将LSTM模型作为参数可变系统,为机器人控制等应用程序提供可靠的状态估计.

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    科学领域:

    • 控制系统工程 控制系统工程
    • 人工智能的人工智能
    • 机器学习 机器学习

    背景情况:

    • 连续时间长短期记忆 (LSTM) 神经网络是序列建模的强大工具,但由于采样输出不规则,对状态估计构成挑战.
    • 现有的状态估计方法经常与LSTM门单元的动态,参数变化的性质以及非统一的数据采集作斗争.
    • 准确的状态估计对于理解和控制复杂的动态系统至关重要,包括由神经网络驱动的系统.

    研究的目的:

    • 开发一种采样数据状态估计器设计方法,用于具有不规则采样输出数据的连续时间LSTM神经网络.
    • 将LSTM神经网络建模为依赖其门单元的连续时间线性参数变化 (LPV) 系统.
    • 在机器人学背景下证明拟议的状态估计方法的实际适用性.

    主要方法:

    • 分析了LSTM结构以得出其动态方程,使其能够作为连续时间LPV系统表示.
    • 采样数据的Luenberger和Arcak类型状态估计器设计方法是使用线性矩阵不等式 (LMIs) 制定的.
    • 该设计利用LSTM门单元的特定特性,以确保有效的状态估计.

    主要成果:

    • 成功设计了一种用于具有不规则输出的连续时间LSTM的新型采样数据状态估计器.
    • 拟议的方法将LSTM模型作为LPV系统,以促进已建立的控制设计技术的应用.
    • 一个数值示例证实了绝对稳定性分析,并且使用机器人操纵者的行为生成模型进行实践演示验证了该方法.

    结论:

    • 开发的状态估计器提供了一个有效的解决方案,用于估计用不规则采样数据的连续时间LSTM的状态.
    • LPV系统建模方法为设计复杂神经网络架构的状态估计器提供了强大的框架.
    • 该方法对现实世界的应用有很大的希望,特别是在需要准确状态反的机器人和控制系统中.