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Related Concept Videos

Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

269
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...
269
Convergence of Fourier Series01:21

Convergence of Fourier Series

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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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Trigonometric Fourier series01:17

Trigonometric Fourier series

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Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
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Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

462
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.
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

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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]...
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Discrete Fourier Transform01:15

Discrete Fourier Transform

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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 24, 2025

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
03:31

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications

Published on: December 15, 2023

451

Enhancing Object Detection With Fourier Series.

Jin Liu, Zhongyuan Lu, Yaorong Cen

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |March 3, 2025
    PubMed
    Summary
    This summary is machine-generated.

    Fourier Series Object Detection (FSD) enhances object detection by encoding outlines as Fourier series, preserving detailed shapes. This novel approach improves accuracy on benchmark datasets, outperforming existing state-of-the-art methods.

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    Area of Science:

    • Computer Vision
    • Image Analysis
    • Machine Learning

    Background:

    • Traditional object detection models struggle to retain intricate object outline details.
    • Loss of fine contour information limits performance, especially for non-standard object shapes.

    Purpose of the Study:

    • To introduce a novel object detection method that preserves detailed object outline information.
    • To improve feature extraction and descriptive capabilities for complex object geometries.

    Main Methods:

    • Developed Fourier Series Object Detection (FSD) which encodes object outlines using one-dimensional periodic Fourier series.
    • Constructed a Fourier Series Model (FSM) to regress Fourier series for objects.
    • Implemented Rolling Optimization Matching for Fourier loss to stabilize training.

    Main Results:

    • Achieved AP50 of 73.3% on the DOTA 1.5 dataset, exceeding the state-of-the-art by 6.44%.
    • Attained AP50 of 97.25% on the UCAS dataset, surpassing existing methods.
    • Demonstrated improved feature extraction for non-rectangular and elongated objects.

    Conclusions:

    • FSD effectively retrieves detailed object outlines, enhancing detection accuracy.
    • Introduced Fourier power spectrum and Fourier vector for richer semantic scene representation.
    • Paved a new direction for the evolution of object detection methodologies.