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Related Concept Videos

Discrete-time Fourier transform01:26

Discrete-time Fourier transform

324
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...
324
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

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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...
261
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

318
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...
318
Discrete Fourier Transform01:15

Discrete Fourier Transform

285
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...
285
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

268
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]...
268
Properties of DTFT II01:24

Properties of DTFT II

199
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.
199

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Related Experiment Video

Updated: Jul 4, 2025

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DctViT: Discrete Cosine Transform meet vision transformers.

Keke Su1, Lihua Cao2, Botong Zhao3

  • 1Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, 130033, Jilin, China; University of Chinese Academy of Sciences, Beijing, 100049, China.

Neural Networks : the Official Journal of the International Neural Network Society
|February 1, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces DctViT, a hybrid network combining CNNs and Vision Transformers (ViTs) for improved image recognition. DctViT achieves state-of-the-art accuracy on ImageNet and COCO datasets with reduced computational costs.

Keywords:
Computer visionDeep learningDiscrete cosine transformImage classificationVision transformer

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Area of Science:

  • Computer Vision
  • Deep Learning
  • Artificial Intelligence

Background:

  • Vision Transformers (ViTs) excel at capturing long-range dependencies via self-attention.
  • Convolutional Neural Networks (CNNs) are effective at extracting local features.
  • Hybrid approaches combining CNNs and ViTs offer potential for balanced performance and computational efficiency.

Purpose of the Study:

  • To propose a novel hybrid CNN-Transformer network for enhanced vision tasks.
  • To introduce a new feature map resolution reduction technique, DCT-Attention Down-sample (DAD).
  • To evaluate the performance of the proposed DctViT model on benchmark datasets.

Main Methods:

  • Developed a hybrid network integrating CNNs for local feature extraction and Transformers for long-range dependency modeling.
  • Proposed the DCT-Attention Down-sample (DAD) module, utilizing Discrete Cosine Transform and self-attention for feature map reduction.
  • Trained and evaluated the DctViT-L model on ImageNet 1K and DctViT-B as a backbone for RetinaNet on COCO val2017.

Main Results:

  • DctViT-L achieved 84.8% top-1 accuracy on ImageNet 1K, surpassing existing state-of-the-art models like CMT and Next-ViT.
  • The DctViT-B backbone improved RetinaNet's mAP to 46.8% on COCO val2017, outperforming CMT-S and SpectFormer.
  • Both configurations demonstrated superior performance with lower computational costs compared to baseline models.

Conclusions:

  • The proposed hybrid DctViT architecture effectively leverages the strengths of both CNNs and Transformers.
  • DAD module offers an efficient method for feature map resolution reduction in vision models.
  • DctViT presents a promising direction for developing high-performance, computationally efficient vision systems.