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What is the inverse fourier transformation of: $ \frac{2+jΩ}{1+jΩ}$ ?

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Taking Partial fraction and writing $$1+\frac{1}{1+jΩ}$$

Now taking Inverse Fourier Transformation

$$F^{-1}(1+\frac{1}{1+jΩ})$$ $$=F^{-1}(1)+F^{-1}(\frac{1}{1+jΩ})$$

$$=\delta(t) + e^{-t}H(t)$$

$H(t)% $=$ $Unit Step Function

$\delta(t)$ = Dirac delta function

Link for the help of inverse of 2nd part.

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