Explore BrainMass

Explore BrainMass

    Cosine and Sine Fourier Transforms

    Not what you're looking for? Search our solutions OR ask your own Custom question.

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

    Problem 1: Consider a function f(t) that is zero for t<0 and equals e^-t/2r for t>=0. Find its Cosine and Sine Fourier Transforms A(w) and B(w). Make a nice plot of A(w) and B (w). Find a convenient value of tau.

    Problem 2: Find the Cosine and Sine Fourier Transforms A(w) and B(w) for the sinusoidal pulse f(t) given by

    f(t) = sin(w_0 * t) for-t_0 / 2 <= t <= t_0 / 2

    and f(t) = 0 outside this range. Make plots of B(w) for cases where
    (i) T = 2pie/w_0 << t_0
    (ii) T = 2pie/w_0 = t_0
    (iii) T = 2pie / w_0 >> t_0

    Problem 3: Now suppose that a pulse of duration t_0 as in Problem 2 contains two sine waves, ie.

    f_2 (t) = sin(w_0 t) + sin(w_1 t) for - t_0 / 2 <= t <= t_0/2

    and f(t) = 0 outside this range. Use the result from Problem 2 to write down (no more evaluation of integrals needed) the Cosine and Sine Fourier Transforms A(w) and B(w) for f_2(t).

    © BrainMass Inc. brainmass.com March 4, 2021, 6:12 pm ad1c9bdddf
    https://brainmass.com/physics/mirrors/cosine-sine-fourier-transforms-34422

    Attachments

    Solution Preview

    Hello and thank you for posting your question to Brainmass!

    The solution ...

    Solution Summary

    The solution to problem (1) includes three pages of calculations neatly formatted in an attached Word document and graphs for A(w), for tau = 0.5 and B(w) for the same value of tau. The calculations and answers for problem (2) and (3) are formatted and explained. 12 pages.

    $2.49

    ADVERTISEMENT