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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 Fourier Transform01:15

Discrete Fourier Transform

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...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

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...
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.
For a discrete-time periodic signal x[n]...
Relation of DFT to z-Transform01:20

Relation of DFT to z-Transform

The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the terms of...
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.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...

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Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy
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Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy

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Image texture characterization using the discrete orthonormal S-transform.

Sylvia Drabycz1, Robert G Stockwell, J Ross Mitchell

  • 1Department of Electrical and Computer Engineering, University of Calgary, 2500 University Dr NW, Calgary, Alberta, T2N 1N4, Canada.

Journal of Digital Imaging
|August 5, 2008
PubMed
Summary

A new discrete, orthonormal space-frequency transform (DOST) offers efficient image texture analysis. This method provides rotationally invariant features, outperforming wavelet-based approaches for texture classification.

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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Area of Science:

  • Image processing
  • Computer vision
  • Signal analysis

Background:

  • Texture characterization is crucial for image analysis.
  • Existing methods like wavelet transforms have limitations.
  • Fourier frequency domain analysis offers potential for texture analysis.

Purpose of the Study:

  • To introduce an efficient image texture characterization method using the Discrete Orthonormal Space-Frequency Transform (DOST).
  • To develop a 2D frequency-domain implementation of DOST for dyadic frequency sampling.
  • To demonstrate DOST's capability in extracting rotationally invariant texture features for accurate classification.

Main Methods:

  • Developed a 2D frequency-domain implementation of the DOST.
  • Created a rapid approach for local spatial frequency information extraction.
  • Combined DOST components to generate rotationally invariant texture features.

Main Results:

  • Successfully characterized horizontal and vertical frequency patterns in synthetic images.
  • Achieved accurate classification of texture patterns using DOST-derived features.
  • Demonstrated DOST's superior performance compared to leading wavelet-based methods.

Conclusions:

  • The DOST provides an efficient and computationally advantageous approach for image texture analysis.
  • DOST combines the benefits of wavelet transforms (multi-scale, efficiency) with Fourier frequency interpretability.
  • This novel transform offers a powerful tool for texture classification and image analysis tasks.