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Related Concept Videos

State Space to Transfer Function01:21

State Space to Transfer Function

294
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
294
Transfer Function to State Space01:23

Transfer Function to State Space

376
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...
376
State Space Representation01:27

State Space Representation

278
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...
278
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

397
The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
397

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Related Experiment Video

Updated: Sep 1, 2025

SSVEP-based Experimental Procedure for Brain-Robot Interaction with Humanoid Robots
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Stimulus-Stimulus Transfer Based on Time-Frequency-Joint Representation in SSVEP-Based BCIs.

Ze Wang, Chi Man Wong, Agostinho Rosa

    IEEE Transactions on Bio-Medical Engineering
    |August 15, 2022
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    Summary

    This study introduces a novel stimulus-stimulus transfer method for brain-computer interfaces (BCIs) using steady-state visual evoked potential (SSVEP). The approach synchronizes SSVEP signals across stimuli, significantly reducing calibration time and improving performance.

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    Area of Science:

    • Neuroscience
    • Biomedical Engineering
    • Signal Processing

    Background:

    • Steady-state visual evoked potential (SSVEP) based brain-computer interfaces (BCIs) require extensive calibration.
    • Transfer learning offers a promising solution but faces challenges in identifying common SSVEP signal components across diverse stimuli.

    Purpose of the Study:

    • To develop a novel method for synchronizing and transferring SSVEP signal components across different stimuli.
    • To reduce the need for extensive calibration in SSVEP-based BCIs.

    Main Methods:

    • A time-frequency-joint representation is proposed to synchronize SSVEP signals from different stimuli.
    • Multi-channel adaptive Fourier decomposition (MAFD) is employed for adaptive, simultaneous decomposition of SSVEP signals.
    • Common components are identified and transferred across stimuli.

    Main Results:

    • A simulation study validated the stimulus-stimulus transfer method's ability to extract and transfer common components.
    • Using calibration data from eight source stimuli, SSVEP templates for 32 target stimuli were generated.
    • The information transfer rate (ITR) for stimulus-stimulus transfer recognition improved from 95.966 bits/min to 123.684 bits/min.

    Conclusions:

    • The proposed method effectively extracts and transfers common SSVEP components, achieving good classification performance without target stimulus calibration data.
    • This approach offers a synchronization perspective for SSVEP signal analysis and modeling.
    • The method reduces calibration time, enhancing user comfort and facilitating real-world BCI applications.