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Related Concept Videos

Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

298
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]...
298
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

346
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...
346
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

292
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
292
Properties of DTFT II01:24

Properties of DTFT II

220
In the study of discrete-time signal processing, understanding the properties of the Discrete-Time Fourier Transform (DTFT) is crucial for analyzing and manipulating signals in the frequency domain. Several properties, including frequency differentiation, convolution, accumulation, and Parseval's relation, offer powerful tools for signal analysis.
The frequency differentiation property is illustrated by considering a DTFT pair and differentiating both sides with respect to ω.
220
Discrete Fourier Transform01:15

Discrete Fourier Transform

322
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...
322
Convergence of Fourier Series01:21

Convergence of Fourier Series

170
The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
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Updated: Jul 19, 2025

Network Analysis of the Default Mode Network Using Functional Connectivity MRI in Temporal Lobe Epilepsy
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CTFNet: Long-Sequence Time-Series Forecasting Based on Convolution and Time-Frequency Analysis.

Zhiqiang Zhang, Yuxuan Chen, Dandan Zhang

    IEEE Transactions on Neural Networks and Learning Systems
    |August 17, 2023
    PubMed
    Summary
    This summary is machine-generated.

    CTFNet, a novel neural network, enhances long-sequence time-series forecasting (LSTF) by integrating time-domain (TD) and frequency-domain (FD) feature extraction. This approach significantly reduces prediction errors for both univariate and multivariate time series.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Time-Series Analysis

    Background:

    • Current state-of-the-art (SOTA) methods for long-sequence time-series forecasting (LSTF) struggle with capturing long-term dependencies and exhibit high computational complexity.
    • Existing models often face information utilization bottlenecks, limiting their effectiveness in complex LSTF tasks.

    Purpose of the Study:

    • To propose CTFNet, a lightweight single-hidden layer feedforward neural network (SLFN), designed to overcome the limitations of current LSTF methods.
    • To enhance feature extraction and reduce computational complexity in LSTF through a novel combination of convolution mapping and time-frequency decomposition.

    Main Methods:

    • CTFNet employs a time-domain (TD) feature mining strategy using matrix factorization to capture long-term correlations among sample points.
    • Multitask frequency-domain (FD) feature mining is utilized to extract diverse frequency information while minimizing data loss, integrating multiscale dilated convolutions for global and local context.
    • The model is designed for high efficiency, featuring short training times and fast inference speeds.

    Main Results:

    • Empirical studies on nine benchmark datasets demonstrate CTFNet's superior performance compared to SOTA methods.
    • CTFNet achieved a reduction in prediction error of 64.7% for multivariate time series and 53.7% for univariate time series.
    • The proposed method effectively breaks data utilization bottlenecks and ensures the integrity of feature extraction.

    Conclusions:

    • CTFNet offers a significant advancement in LSTF by effectively addressing feature extraction challenges and computational complexity.
    • The model's ability to integrate TD and FD analysis provides a robust framework for accurate and efficient long-sequence forecasting.
    • CTFNet represents a promising, highly efficient solution for various LSTF applications.