Fourier Transform Rect function

Discussion in 'Math' started by yoamocuy, Feb 2, 2012.

  1. yoamocuy

    Thread Starter Active Member

    Oct 7, 2009
    80
    0
    1. The problem statement, all variables and given/known data
    Find the fourier transform of A∏((t-T)/(2*T)).


    2. Relevant equations
    V(F)=∫v(t)*e-j*2*pi*f*t


    3. The attempt at a solution
    ∫(A*e-j*2*pi*f*t,t,0,2T)
    = A*sin(4*f*pi*T)/(2*f*pi*T)+j(A*cos(4*pi*f*T)-A)/(2*pi*f)
    =2*A*T*sinc(4*f*T)+j*(A*cos(4*pi*f*T)-A)/(2*pi*f)

    The answer's supposed to be = 2*A*T*sinc(2*f*T)*e-j*2*pi*f*T

    Is everything I've done so far ok? How do I go about simplifying the cos into an e log?
     
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