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An inverse fourier transform

  1. Jan 9, 2012 #1
    1. The problem statement, all variables and given/known data
    (part of a problem)
    Find the inverse fourier of F(w) = (3jw+9)/((jw)^2+6jw+8)
    where w is the angular frequency, w=2pi * f = 2*pi/T

    2. Relevant equations
    The fourier transfrom and its properties i guess.
    Also the exponential FT common pair exp(-at)u(t) <-> 1/(jw+a)
    where exp is the exponential function and u(t) the unit step function


    3. The attempt at a solution
    I factored out the denominator in a hope that the 3jw+9 would cancel out with a possible root of jw=-3 , but the roots are -2 and -4.
    I've been trying to seperate F into a product of easy transformable parts, to take advantage of the convolution property : x(t) [convolve] f(t) = X(w)F(w) , but i cant get rid of the nominator to apply the exponential fourier pair.
    Any hints?
     
  2. jcsd
  3. Jan 9, 2012 #2
    If the nominator was a constant, i could break it into simple fractions.
    Can you do it if it's not a constant?
     
  4. Jan 9, 2012 #3
    ^
    Ah,nevermind, you can.
    case closed.
     
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