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copied!<p>I am still learning Mathematica myself, but here is what I came up with..</p> <p>First we define the piecewise function (I am using the example from the Wikipedia page)</p> <pre><code>f[x_] := Piecewise[{{1, -0.5 <= x <= 0.5}}, 0] </code></pre> <p><img src="https://i.stack.imgur.com/d0TPs.png" alt="piecewise_function"></p> <p>Lets plot the function:</p> <pre><code>Plot[f[x], {x, -2, 2}, PlotStyle -> Thick, Exclusions -> None] </code></pre> <p><img src="https://i.stack.imgur.com/tTUxo.png" alt="function_plot"></p> <p>Then we write the function that defines the convolution of <code>f</code> with itself:</p> <pre><code>g[t_] = Integrate[f[x]*f[t - x], {x, -Infinity, Infinity}] </code></pre> <p><img src="https://i.stack.imgur.com/eFxuV.png" alt="convolution_integral"></p> <p>and the plot:</p> <pre><code>Plot[g[t], {t, -2, 2}, PlotStyle -> Thick] </code></pre> <p><img src="https://i.stack.imgur.com/Xv8yY.png" alt="convolution_plot"></p> <hr> <h3>EDIT</h3> <p>I tried to do the same in MATLAB/MuPad, I wasn't as successful:</p> <pre><code>f := x -> piecewise([x < -0.5 or x > 0.5, 0], [x >= -0.5 and x <= 0.5, 1]) </code></pre> <p><img src="https://i.stack.imgur.com/whfpS.png" alt="func_def"></p> <pre><code>plot(f, x = -2..2) </code></pre> <p><img src="https://i.stack.imgur.com/uB84D.png" alt="func_plot"></p> <p>However when I try to compute the integral, it took almost a minute to return this:</p> <pre><code>g := t -> int(f(x)*f(t-x), x = -infinity..infinity) </code></pre> <p><img src="https://i.stack.imgur.com/zeZQ7.png" alt="convolution"></p> <p>the plot (also took too long)</p> <pre><code>plot(g, t = -2..2) </code></pre> <p><img src="https://i.stack.imgur.com/pnY90.png" alt="convolution_plot"></p> <p>Note the same could have been done from inside MATLAB with the syntax:</p> <pre><code>evalin(symengine,'<MUPAD EXPRESSIONS HERE>') </code></pre>

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