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## Convolution Tool

Simulate the convolution of different functions

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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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