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Related Concept Videos

Discrete-time Fourier transform01:26

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

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...
Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
Discrete Fourier Transform01:15

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at zero. It...

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Extracting Visual Evoked Potentials from EEG Data Recorded During fMRI-guided Transcranial Magnetic Stimulation
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Time-frequency feature extraction method for EEG signals utilizing fractional-order transient-extracting transform.

Sheng-Wei Fei1, Yi-Bo Hu1, Jia-le Chen1

  • 1College of Mechanical Engineering, Donghua University, Lane 2999, Renmin North Road, Songjiang 201620 Shanghai, People's Republic of China.

Biomedical Physics & Engineering Express
|May 12, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new Fractional-order transient-extracting transform (FOTET) for improved electroencephalographic (EEG) signal analysis in motor imagery (MI) tasks. FOTET enhances feature extraction, boosting brain-computer interface (BCI) performance.

Keywords:
electroencephalogram (EEG) signalsfractional-order transient-extracting transformmotor imagerytime–frequency analysis (TFA)

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Area of Science:

  • Neuroscience
  • Signal Processing
  • Biomedical Engineering

Background:

  • Extracting transient features from electroencephalographic (EEG) signals during motor imagery (MI) is challenging.
  • Accurate extraction of these features is crucial for effective brain-computer interface (BCI) performance.

Purpose of the Study:

  • To propose a novel Fractional-order transient-extracting transform (FOTET) for enhanced EEG signal feature extraction.
  • To improve the accuracy and efficiency of capturing transient neural activity during MI tasks.

Main Methods:

  • Introduced a fractional-order transient extracting operator and an iterative optimization process within FOTET.
  • Developed a method to balance time-frequency resolution by adjusting the fractional order parameter.
  • Utilized DenseNet-LSTM for classification of four-class MI tasks using extracted features.

Main Results:

  • FOTET effectively extracts transient features from noisy EEG signals, enabling better discrimination between different MI classes.
  • Achieved a classification accuracy of 96.71% with FOTET combined with DenseNet-LSTM.
  • Demonstrated superior performance compared to traditional time-frequency analysis (TFA) methods.

Conclusions:

  • FOTET significantly enhances the extraction of transient features in EEG signals for MI.
  • The proposed method offers a superior approach for EEG signal analysis in BCI applications.
  • FOTET's ability to handle noisy environments and improve classification accuracy validates its effectiveness.