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Transformations of Functions III01:20

Transformations of Functions III

304
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...
304
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

13.7K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
13.7K
Transformations of Functions I01:29

Transformations of Functions I

286
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...
286
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

1.3K
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...
1.3K
Transformations of Functions II01:29

Transformations of Functions II

269
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,...
269
Basic Operations on Signals01:22

Basic Operations on Signals

1.3K
Basic signal operations include time reversal, time scaling, time shifting, and amplitude transformations. These operations are fundamental in signal processing and analysis.
Time Reversal mirrors a continuous-time signal about the vertical axis at t=0. This is achieved by substituting t with −t. For example, if a signal x(t) is considered, the time-reversed signal is x(−t). This operation can be graphically represented, showing the mirrored signal.
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Related Experiment Video

Updated: May 3, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

4.7K

A graph theory practice on transformed image: a random image steganography.

V Thanikaiselvan1, P Arulmozhivarman1, S Subashanthini2

  • 1School of Electronics Engineering, VIT University, Vellore 632014, India.

Thescientificworldjournal
|January 24, 2014
PubMed
Summary

This study introduces a novel random image steganography method combining integer wavelet transform (IWT) and graph theory for secure communication. The technique achieves high imperceptibility and embedding capacity, enhancing data security in the digital age.

Related Experiment Videos

Last Updated: May 3, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

4.7K

Area of Science:

  • Computer Science
  • Information Security
  • Digital Image Processing

Background:

  • The information age faces significant security challenges in protecting sensitive data during storage and transmission.
  • Advanced network communication necessitates robust methods for secure information handling.

Purpose of the Study:

  • To develop a secure random image steganography technique for enhanced data protection.
  • To combine Integer Wavelet Transform (IWT) with graph theory for improved steganographic performance.

Main Methods:

  • Cover image is transformed into wavelet coefficients using Integer Wavelet Transform (IWT).
  • Secret image data is embedded into randomly selected coefficients guided by graph theory principles.
  • The stegoimage is reconstructed by applying the inverse Integer Wavelet Transform (IWT).

Main Results:

  • The proposed method achieves a high Peak Signal to Noise Ratio (PSNR) of up to 44 dB for 266,646 bits.
  • Demonstrates high imperceptibility due to high PSNR values.
  • Exhibits high embedding capacity via an adaptive embedding scheme.

Conclusions:

  • The developed random image steganography method offers high imperceptibility and embedding capacity.
  • The integration of graph theory enhances robustness against blind attacks.
  • This technique provides a secure solution for transmitting private information in the digital era.