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Related Concept Videos

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...
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...
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 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...

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Related Experiment Video

Updated: May 7, 2026

Simultaneous Scalp Electroencephalography EEG, Electromyography EMG, and Whole-body Segmental Inertial Recording for Multi-modal Neural Decoding
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FourierMask: Explain EEG-Based End-to-End Deep Learning Models in the Frequency Domain.

Hanqi Wang, Jingyu Zhang, Kun Yang

    IEEE Journal of Biomedical and Health Informatics
    |September 18, 2025
    PubMed
    Summary

    FourierMask is the first frequency-domain explanation framework for electroencephalography (EEG) deep learning models. It enhances transparency by linking model decisions to spectral biomarkers, improving neuromedicine and brain-computer interface applications.

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    Area of Science:

    • Neuroscience
    • Machine Learning
    • Signal Processing

    Background:

    • Deep learning models for electroencephalography (EEG) analysis are increasingly used, but their decision-making processes remain opaque.
    • Understanding how these models interpret time-series EEG signals is crucial for reliable applications.
    • The frequency domain offers advantages for EEG analysis due to its correlation with cognitive states and ability to capture long-range dependencies, yet it's underexplored for model explanation.

    Purpose of the Study:

    • To introduce FourierMask, a novel mask perturbation framework for explaining EEG-based end-to-end deep learning models in the frequency domain.
    • To enhance the transparency and interpretability of complex EEG models.
    • To identify key frequency biomarkers driving model predictions.

    Main Methods:

    • Developed FourierMask, a framework utilizing Fourier-based domain transformation for direct spectral component manipulation.
    • Implemented a learnable mask mechanism to jointly model spectral-spatial couplings for EEG explanation.
    • Employed a perturbation generator with a target alignment loss and cluster-aware regularization to ensure natural perturbations and minimize distribution shift.

    Main Results:

    • FourierMask achieved significant accuracy drop gaps: 36.0% at the group-level and 17.8% at the instance-level, outperforming LIME and easyPEASI.
    • Demonstrated superior performance compared to existing methods in quantifying the importance of frequency components.
    • Validated effectiveness across multiple EEG deep learning architectures (EEGNet, TSCeption, DeepConvNet).

    Conclusions:

    • FourierMask provides a model-agnostic, plug-and-play solution for enhancing the transparency of EEG deep learning models.
    • Effectively links model predictions to specific frequency biomarkers, offering insights into cognitive states.
    • Presents potential applications in advancing neuromedicine and brain-computer interfaces through interpretable EEG analysis.