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Fourier Transform

  1. Dec 11, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-12-11_12-32-47.png

    2. Relevant equations
    if x(t) --> X(W)
    then
    x(-t) --> X(-W)
    and
    x(t+a)-->ejwX(W)

    3. The attempt at a solution
    upload_2017-12-11_12-33-14.png
    I'm getting right answer for 1st part. For second part book says right answer is C.
    Where am I wrong?
     
  2. jcsd
  3. Dec 11, 2017 #2
    First you calculate x(t) by inverse fourier tansform then by substituting t=-t and t=-t-1 you will get the result
     
  4. Dec 11, 2017 #3
    So as per rules
    if f(t)----> Fourier---> F(jw)
    then f(t-to) ----> estoF(jw)
    So then if there is now any more x(3(t-to)) then does the change reflect in esto also or is that a constant and only F(jw) becomes 1/|a| F(jw/a)?
     
  5. Dec 12, 2017 #4
    This is what I tried for second part. But book answer is c
     
  6. Dec 12, 2017 #5
    Yes you can apply this property. i told you in previous post to recheck ur answer by that method.
     
  7. Dec 12, 2017 #6
    Thanks. But I dont know how to use inverse fourier method. What answer are you getting? B or C?
    It could be book answer is wrong.

    I wanted to ask a doubt on fourier?
    If we have to use time shift property followed by time scaling property then does the exponential part also change?
    upload_2017-12-12_15-49-6.png
    I can't find any solved examples. In laplace there were a few unsolved examples but then my answer matched when I didn't consider e^(-Ts) as part of new F(S). As in the second circle drawn above.
     

    Attached Files:

  8. Dec 12, 2017 #7
    A
    Just multiply by e^-jw to the answer you got in previous problem.In only time shift exponential term come you can do it by simple integration
     
  9. Dec 12, 2017 #8
    That gives answer but should it be e^-jw or e^(+jw)
    since x(-t-1) = x(-(t+1))
    So I'm not sure how to go ahead with this. Should it be +jw or -jw?
     
  10. Dec 12, 2017 #9
    -Jw
     
  11. Dec 12, 2017 #10
    In original post I've used time shift property first and then time scaling. Can u help me as to why i'm not getting right answer there? I've pasted pic.
     
  12. Dec 12, 2017 #11
  13. Dec 12, 2017 #12
    You have done right but you choose option b and option b is not matching to you result may be in option c there is print mistake with minus sing in first term.
     
  14. Dec 12, 2017 #13
    Thanks.
     
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