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Math Help - Inverse fourier Transform of 1/(1+.5jw)

  1. #1
    Member moonnightingale's Avatar
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    Inverse fourier Transform of 1/(1+.5jw)

    Hi the inverse fourier transform of

    1/(alpha+jw) is u(t)exp(-alpha x t)

    but what if there is some term with jw like 1/(1+.5jw)
    how it will be catered
    I could not see such example in any fourier transform table

    Plz guide me
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  2. #2
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    Re: Inverse fourier Transform of 1/(1+.5jw)

    Quote Originally Posted by moonnightingale View Post
    Hi the inverse fourier transform of

    1/(alpha+jw) is u(t)exp(-alpha x t)

    but what if there is some term with jw like 1/(1+.5jw)
    how it will be catered
    I could not see such example in any fourier transform table

    Plz guide me
    Just build the fraction by multiplying by \frac{2}{2}

    \frac{1}{1+.5jw}=\frac{2}{2}\cdot \frac{1}{1+.5jw}=\frac{2}{2+jw}

    Just remember that the inversve transform is linear so

    F^{-1}\left( \frac{2}{2+jw} \right) =2F^{-1}\left( \frac{1}{2+jw} \right)
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