F_r(s) =
Two sided laplace transform
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Hello, is there any function that generates two sided laplace transform?
回答（1 个）
No, there is not, at least not directly.
However, the two-sided Laplace transform of f(t) can be developed by
- expressing f(t) as the sum of a strictly left-sided signal and a strictly right-sided signal
- computing the two-sided transform of each part. The two-sided transform of the strictly right-sided signal is the same as its one-sided transform. The two-sided transform of the strictly left-sided signal can be found from the unilateral transform using the time reversal property.
- summing the transforms after verifying their respective regions of convergence intersect
Example
syms a b t real
f(t) = exp(-a*t)*heaviside(t) - exp(-b*t)*heaviside(-t);
1. define right- and left-sided parts
f_r(t) = exp(-a*t)*heaviside(t);
f_l(t) = -exp(-b*t)*heaviside(-t);
2. two-sided transforms
syms s
F_r(s) = laplace(f_r(t),t,s)
The ROC of F_r(s) is Re(s) > -a
F_l(s) = subs(laplace(f_l(-t),t,s),s,-s)
The ROC of F_l(s) is Re(s) < -b
3. The two-sided transform of f(t) is
F(s) = F_l(s) + F_r(s)
[num,den] = numden(F(s));
F(s) = num/den
The ROC of F(s) is -a < Re(s) < -b, as long as -b > -a.
If -b <= -a, then the two-sided transform of f(t) does not exist.
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