I want to calculate the convolution sum of the continuous unit pulse with itself, but I don't know how I can define this function $$ \delta(t) = \begin{cases} 1, 0 \le t \lt 1 \\ 0, otherwise \end{cases}$$ in Matlab.
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$\begingroup$Use the rectangularPulse function.
Or you can define arbitrary piecewise functions in a number of ways, e.g.
ix=x<0
y(ix)=0
ix=x>=1
y(ix)=0
ix=0<=x&x<1
y(ix)=1
$\endgroup$ 2 $\begingroup$For symbolic math you can take advantage of MuPAD within Matlab. See the documentation for piecewise. You can use this function to concisely produce the example in your question:
pw = evalin(symengine,'piecewise([t >= 0 and t < 1, 1],[Otherwise, 0])')And you can evaluate it for vector inputs using subs like this:
subs(pw,'t',[1/2 1 0])which returns
ans =
[ 1, 0, 1]See the documentation for piecewise for more examples of how to define piecewise functions. There are other ways to call MuPAD functions from Matlab – see here. Of course this method is not meant for performance, so you shouldn't rely on it being as fast as floating-point methods.
Create a MATLAB function with the following code
function d = delta(t)
if t >= 1 d = 0;
else if t < 0 d = 0;
else d = 1;
end
endAnd use delta for whatever reasons you want.
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