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Introduction: This application demonstrates the convolution of a signal by a system. Various signals and systems may be selected, and the output of the convolution sum is displayed.


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This application demonstrates the convolution sum, as a system (green) that processes a signal (red). As the signal slides past the system, the system displays the current output (as the sum of the entire system multiplied by the overlapping portion of the signal) and the total output (as the sum over time).

This application demonstrates the effects of various systems on various signals. For example, a high-pass filter and a low-pass filter are included, and the filtering properties of these systems may be demonstrated by convolution with a high-frequency sinusoid signal and a low-frequency sinusoid signal. Another interesting convolution is the use of a cardinal sine ("sinc") system to convolve a square pulse; the output closely resembles the square pulse, with characteristically sharp discontinuities (the "Gibbs effect") apparent just before and after the sharp edges of the square pulse.

An interesting property of the convolution sum is that swapping the signal and the system produces the same output. This property may be demonstrated by selecting any signal and any system; noting the total output of the convolution; clicking the "Swap" button; and observing that the total output remains the same for the swapped signal and system.

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(c) 2015, David Stein. All rights reserved.