I am trying to calculate the convolution of
x(t) = 1, -1<=t<=1
x(t) = 0, outside
with itself using the definition.
http://en.wikipedia.org/wiki/Convolution
I know how to do using the Matlab function conv, but I want to use the integral definition. My knowledge of Matlab and WolframAlpha is very limited.
I am still learning Mathematica myself, but here is what I came up with..
First we define the piecewise function (I am using the example from the Wikipedia page)
f[x_] := Piecewise[{{1, -0.5 <= x <= 0.5}}, 0]
Lets plot the function:
Plot[f[x], {x, -2, 2}, PlotStyle -> Thick, Exclusions -> None]
Then we write the function that defines the convolution of f
with itself:
g[t_] = Integrate[f[x]*f[t - x], {x, -Infinity, Infinity}]
and the plot:
Plot[g[t], {t, -2, 2}, PlotStyle -> Thick]
I tried to do the same in MATLAB/MuPad, I wasn't as successful:
f := x -> piecewise([x < -0.5 or x > 0.5, 0], [x >= -0.5 and x <= 0.5, 1])
plot(f, x = -2..2)
However when I try to compute the integral, it took almost a minute to return this:
g := t -> int(f(x)*f(t-x), x = -infinity..infinity)
the plot (also took too long)
plot(g, t = -2..2)
Note the same could have been done from inside MATLAB with the syntax:
evalin(symengine,'<MUPAD EXPRESSIONS HERE>')