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Properties of the Fourier Transform

February 2, 2019 by 3200 Creative

Properties of the Fourier Transform

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  1. Question 1 of 5
    1. Question

    If signals x(t) and y(t) have Fourier transforms X(\Omega) = \frac{1}{j\Omega + 1} and Y(\Omega) = \frac{1}{j\Omega +3}, what is the Fourier transform of z(t) = x(t)-2y(t)?

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  2. Question 2 of 5
    2. Question

    A signal x(t) = e^{-t}u(t) is applied to a linear time-invariant system with impulse response  h(t) = e^{-3t}u(t). What is the Fourier transform of the output y(t) = x(t)*h(t)? Hint: recall that e^{-at}u(t) has Fourier transform \frac{1}{j\Omega + a}.

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  3. Question 3 of 5
    3. Question

    A signal x(t) = e^{-t}u(t) has Fourier transform X(\Omega) = \frac{1}{j\Omega + 1}. Use the properties of the Fourier transform to find the signal z(t) with Fourier transform Z(\Omega) = \frac{e^{-j2\Omega}}{j\Omega + 1}.

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  4. Question 4 of 5
    4. Question

    A signal x(t) = e^{-t}u(t) has Fourier transform X(\Omega) = \frac{1}{j\Omega + 1}. Use the properties of the Fourier transform to find the signal z(t) with Fourier transform Z(\Omega) = \frac{-j\Omega}{j\Omega + 1}.

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  5. Question 5 of 5
    5. Question

    A signal x(t) = e^{-t}u(t) has Fourier transform X(\Omega) = \frac{1}{j\Omega + 1}. Use the properties of the Fourier transform to find the signal z(t) with Fourier transform Z(\Omega) = \frac{1}{j(\Omega-2) + 1}.

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