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Related Concept Videos

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-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.
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Properties of DTFT I01:24

Properties of DTFT I

In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
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Deconvolution01:20

Deconvolution

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Discrete Fourier Transform01:15

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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...
Maximizing the Directional Derivative01:25

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The directional derivative is a central concept in multivariable calculus that describes how a function changes at a given point when moving in a specified direction. This direction is represented by a unit vector, ensuring that only the orientation influences the rate of change. By varying the direction, different rates of change can be observed, demonstrating that the directional derivative depends strongly on the chosen direction.The directional derivative is computed using the gradient...

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Related Experiment Video

Updated: Jun 17, 2026

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
08:42

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method

Published on: September 3, 2021

Adaptive directional wavelet transform based on directional prefiltering.

Yuichi Tanaka1, Madoka Hasegawa, Shigeo Kato

  • 1Department of Information Science, Utsunomiya University, Tochigi, Japan. tanaka@is.utsunomiya-u.ac.jp

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|December 24, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces efficient methods for adaptive directional wavelet transform (WT) using prefiltering. These approaches maintain image coding performance while significantly reducing computational complexity and enabling content-based image retrieval.

Related Experiment Videos

Last Updated: Jun 17, 2026

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
08:42

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method

Published on: September 3, 2021

Area of Science:

  • Image Processing
  • Signal Processing
  • Computer Vision

Background:

  • Adaptive directional wavelet transform (WT) offers superior image coding performance by analyzing diagonal orientations alongside traditional horizontal and vertical directions.
  • Conventional adaptive directional WT methods often incur high computational complexity, limiting their practical application.
  • Efficient computation of transform directions is crucial for balancing performance and speed in image processing.

Purpose of the Study:

  • To develop computationally efficient methods for determining optimal transform directions in adaptive directional WT.
  • To maintain or improve image coding performance while reducing the complexity of adaptive directional WT.
  • To explore the utility of transform direction data for content-based image retrieval applications.

Main Methods:

  • Proposed two novel prefiltering techniques for efficient calculation of adaptive directional WT.
  • Method 1: Prefiltering using a 2-D filter bank.
  • Method 2: Prefiltering using a 1-D directional WT along two fixed directions.

Main Results:

  • The proposed direction calculation methods achieve image coding performance comparable to conventional approaches.
  • Significant reduction in computational complexity compared to existing methods.
  • Transform direction data generated by the proposed methods demonstrates potential for enhancing content-based image retrieval accuracy.

Conclusions:

  • Efficient prefiltering strategies can substantially decrease the computational cost of adaptive directional WT.
  • The proposed methods provide a practical solution for high-performance image coding with reduced complexity.
  • The derived transform direction information offers a valuable feature for content-based image retrieval systems.