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Convolution Tool

Simulate the convolution of different functions

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Version 1.0 - published on 02 Aug 2012

doi:10.4231/D3183420W cite this

This tool is closed source.

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See also

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Available functions for x(t) Available functions for h(t) Plot of x(τ) Plot of h(τ) Plot of h(-τ) Convolution of x(t) and h(t) at t = 1.88 Convolution of x(t) and h(t) at t = 9 Plot of y(t) - convolution of x(t) and h(t)

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Tools

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Abstract

Convolution Tool allows users to compute the convolution of two continuous-time functions. The continuous-time functions in this tool are actually approximated from discrete-time functions with very small time steps.

The following functions are available in Convolution Tool

  • Step
  • Pulse
  • Exponential
  • Ramp
  • Sinusoidal

Convolution Tool presents results that enable the user to understand the steps involved in Graphical Convolution. In other words, the results correspond to the following steps that are used in Graphical Convolution:

  • Replacing t with a new variable τ, to yield x(τ) and h(τ)
  • Flipping h(τ) about the y-axis to get h(-τ)
  • Adding t to -τ which now yields h(-τ+t) or h(t-τ), and then sliding from t=-∞ to t=+∞
  • While sliding t, for each value of t, multiplying the intersection of x(τ) and h(t-τ) and then finding the definite integral of the product using the intersection as the limits of the integral.

For more on Convolution, please refer to the Supporting Docs.

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GNU Octave

References

McLennan, M. (2005), The Rappture Toolkit, http://rappture.org. (2011), Workspace (800x600), DOI: 10254/nanohub-r1242.1. (DOI: 10254/nanohub-r1242.1).

Cite this work

Researchers should cite this work as follows:

  • Ogaga Daniel Odele; Hanjun Xian; Krishna P. C. Madhavan (2012), "Convolution Tool," http://nanohub.org/resources/convn. (DOI: 10.4231/D3183420W).

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