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Homework Statement
F{f(t)} is the Fourier transform of f(t) and L{f(t)} is the Laplace transform of f(t)
why F{f(t)} = L{f(t)} where s = jw in L{f(t)}
The Attempt at a Solution
I suppose the definition of F{f(t)} is
∫[f(t)e^-jwt]dt
where the lower integral limit is -∞ and higher intergral limit is +∞.
And I suppose the definition of L{f(t)} is
∫[f(t)e^-st]dt
where the lower integral limit is -∞ and higher integral limit is +∞.(that is bilateral Laplace transform)
and i think it is obviously to say F{f(t)} = L{f(t)} where s = jw in L{f(t)} just by substitute s = jw in ∫[f(t)e^-st]dt.
My solution is so simple that I can't believe it's a problem assigned by my professor!
Some guy please tell me if I am correct or not, and where it is.
Any reference or advise will be appreciated.
thanks in advance.