Explore BrainMass
Share

Explore BrainMass

    Fourier transform and its properties

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please see the attached file and include an explanation of problem. Thank you.

    1. Compute the Fourier transform for x(t) = texp(-t)u(t)

    2. The linearity property of the Fourier transform is defined as:

    3. Determine the exponential Fourier series for:

    4. Using complex notation, combine the expressions to form a single sinusoid for: cos(10t+ pi/2) + 2cos(10t - pi/3)

    5. The polar notation for the function 1 + e^(j4) is:

    6. The duality property of the Fourier transform is defined as:

    7. A continuous time signal x(t) has the Fourier transform: x(w) = 1/(jwW +b), where b is a constant. Determine the Fourier transform for v(t) = t^2*x(t).

    8. Compute the inverse Fourier transform for X(w) = cos(4w).

    9. A continuous time signal x(t) has the Fourier transform: x(w) = 1/(jw +b), where b is a constant. Determine the Fourier transform for v(t) = x(t) * x(t).

    10. The polar notation for the function 1 + e^(j4) + e^(j2) is:

    © BrainMass Inc. brainmass.com April 3, 2020, 6:09 pm ad1c9bdddf
    https://brainmass.com/math/fourier-analysis/fourier-transform-and-its-properties-195376

    Attachments

    Solution Summary

    The solution explains the Fourier transform and its properties in detail. It also shows how to represent a function using polar notation.

    $2.19

    ADVERTISEMENT