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Related Concept Videos

Transformations of Functions III01:20

Transformations of Functions III

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...
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Convolution computations can be simplified by utilizing their inherent properties.
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Transformations of Functions II01:29

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

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Properties of DTFT I01:24

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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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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...

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Quantifying Intermembrane Distances with Serial Image Dilations
07:45

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Published on: September 28, 2018

Discrete linear canonical transforms based on dilated Hermite functions.

Soo-Chang Pei1, Yun-Chiu Lai

  • 1Graduate Institute of Communication Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan. pei@cc.ee.ntu.edu.tw

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|August 4, 2011
PubMed
Summary
This summary is machine-generated.

A new discrete linear canonical transform (DLCT) approximates the continuous LCT using Hermite functions. This DLCT offers additivity, reversibility, and preserves signal length, outperforming existing methods.

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Area of Science:

  • Signal Processing
  • Optics
  • Mathematical Physics

Background:

  • The Linear Canonical Transform (LCT) is a fundamental tool in signal processing and optics.
  • Existing digital computations of LCT often involve limitations such as oversampling or loss of key properties.

Purpose of the Study:

  • To propose a novel discrete Linear Canonical Transform (DLCT) that accurately approximates the continuous LCT.
  • To evaluate the performance of the proposed DLCT in the time-frequency domain.

Main Methods:

  • Utilizing discrete dilated Hermite functions for the DLCT approximation.
  • Employing the Wigner distribution function to analyze DLCT performance in the time-frequency domain.

Main Results:

  • The proposed DLCT demonstrates additivity and reversibility properties.
  • The DLCT transformation does not require oversampling and preserves signal length, maintaining the area-preserving nature of LCT.
  • The DLCT shows a strong approximation of the continuous LCT.

Conclusions:

  • The developed DLCT provides an efficient and accurate digital method for LCT.
  • This DLCT is suitable for applications in signal processing and optics requiring precise time-frequency analysis.