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Math Help - Fourier transform of x(t)=1

  1. #1
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    Fourier transform of x(t)=1

    Hi all

    I know that the Fourier transform of x(t)=1 is X(jω)=2πδ(ω) by using the duality property.
    This implies:
    \int_{-\infty }^{+\infty }e^{-j\omega t}dt=2\pi\delta(\omega)
    Consequently, for ω≠0:
    \int_{-\infty }^{+\infty }e^{-j\omega t}dt=0
    And as a result:
    \int_{-\infty }^{+\infty }\cos t\: dt=0

    Is this result true?!

    Thanks in advance
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  2. #2
    Senior Member
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    Los Angeles, California
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    Re: Fourier transform of x(t)=1

    No; \delta(\omega)\ne 0.
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