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Related Concept Videos

Upsampling01:22

Upsampling

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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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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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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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Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

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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...
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Discrete-time Fourier transform01:26

Discrete-time Fourier transform

448
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...
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Downsampling01:20

Downsampling

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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Deep Fourier Ranking Quantization for Semi-Supervised Image Retrieval.

Pandeng Li, Hongtao Xie, Shaobo Min

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    Summary
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    This study introduces a novel Fourier-based approach for semi-supervised learning, enhancing deep networks by exploring unlabeled data relationships. The method improves model robustness and generalization, outperforming existing techniques.

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    Area of Science:

    • Computer Science
    • Machine Learning
    • Deep Learning

    Background:

    • Supervised product quantization methods exhibit extreme label dependence.
    • Semi-supervised learning uses unlabeled data to regularize deep networks, but existing methods overlook individual instance variances.
    • This oversight limits exploration of local neighborhood structures, leading to overfitting.

    Purpose of the Study:

    • To introduce a Fourier-based perspective to explore semantic relations in unlabeled data for improved semi-supervised learning.
    • To address the limitations of existing methods that focus on overall distribution consistency and ignore individual instance variances.
    • To enhance the robustness and generalization of deep learning models in semi-supervised settings.

    Main Methods:

    • A novel Phase Mixing (PM) strategy based on Fourier Transform is proposed to manipulate phase components for controlling semantic information proportion.
    • This strategy naturally constructs multi-level similarity neighbors for unlabeled data.
    • A ranking quantization loss is formulated to perceive multi-level semantic variances within neighbor instances.

    Main Results:

    • The proposed method successfully explores semantic relations between unlabeled instances in a self-supervised manner.
    • It constructs multi-level similarity neighbors and perceives multi-level semantic variances, improving model robustness and generalization.
    • Experiments across three semi-supervised settings demonstrated an average improvement of 3.95% over state-of-the-art methods on four datasets.

    Conclusions:

    • The Fourier-based approach effectively alleviates label dependence in semi-supervised learning by leveraging unlabeled data more effectively.
    • The Phase Mixing strategy and ranking quantization loss enhance model performance by capturing subtle semantic variations.
    • This work offers a promising direction for improving deep network regularization and generalization in semi-supervised learning.