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Related Concept Videos

Properties of Fourier Transform II01:24

Properties of Fourier Transform II

The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
Transformations of Functions III01:20

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Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...
Transformations of Functions II01:29

Transformations of Functions II

Transformations in mathematics alter the position or orientation of a function’s graph while preserving its fundamental shape. One important type of transformation is the horizontal shift, which involves modifying the input variable within a function’s equation. This operation affects where outputs occur along the horizontal axis but does not alter the function’s overall structure.A horizontal shift is achieved by replacing the input variable x with either x + c or x - c, where c is a constant.
Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
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Transformations of Functions I01:29

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A function's graph can be modified by changing its position or size without altering its overall shape. These transformations allow the graph to be moved across the coordinate plane while preserving its pattern and structure. One of the most common transformations is shifting, which repositions the graph without distorting it.When the output of a function is adjusted by adding or subtracting a constant, the graph shifts vertically. A positive value moves the graph upward, while a negative value...
Properties of the z-Transform I01:17

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The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...

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Related Experiment Video

Updated: May 29, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

The adaptive hough transform.

J Illingworth1, J Kittler

  • 1Department of Electronic and Electrical Engineering, University of Surrey, Guildford GU2 5XH, England.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

The Adaptive Hough Transform (AHT) offers a more efficient method for 2-D shape detection than the standard Hough Transform (HT). This novel approach significantly reduces storage and computational needs while remaining robust to noise and complex images.

Related Experiment Videos

Last Updated: May 29, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

  • Computer Vision
  • Image Processing
  • Pattern Recognition

Background:

  • The standard Hough Transform (HT) is a widely used method for detecting shapes in images.
  • However, traditional HT implementations can be computationally intensive and require significant memory.
  • There is a need for more efficient and robust shape detection algorithms.

Purpose of the Study:

  • To introduce the Adaptive Hough Transform (AHT) as an improved method for 2-D shape detection.
  • To demonstrate the AHT's superiority in terms of storage and computational efficiency compared to the standard HT.
  • To showcase the AHT's robustness against noise and its applicability to complex images.

Main Methods:

  • The Adaptive Hough Transform (AHT) utilizes a small accumulator array.
  • A flexible, iterative "coarse to fine" accumulation and search strategy is employed.
  • The method identifies significant peaks in Hough parameter spaces for shape detection.

Main Results:

  • The AHT significantly reduces storage and computational requirements compared to the standard HT.
  • The method effectively identifies linear and circular segments in images.
  • The AHT demonstrates robustness to extraneous noise and handles complex images with multiple shapes.

Conclusions:

  • The Adaptive Hough Transform (AHT) provides a substantially more efficient implementation of the Hough Transform for 2-D shape detection.
  • The AHT is a robust and versatile tool for analyzing images, including those with noise and multiple shapes.