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How can I derive the fourier transform of

                                   g1(t) = {A cos(2πfc t),−T/2 < t <T/2
                                            0,               elsewhere 

and;

                                  g2(t) = cos(t), −∞ < t < ∞

my answer for g1 is;

∫ g(t)exp(-j*2*pi*f*t)dt = ∫ Acos(2*pi*fc*t)exp(-j*2*pi*f*t)dt

   =∫ 1/2A (exp(j*2*pi*fc*t)+exp(-j*2*pi*fc*t))exp(-j*2*pi*f*t)dt

   =∫1/2A(exp(j*2*pi*fc*t)exp(-j*2*pi*fc*t)+∫1/2A(exp        (-j*2*pi*fc*t)exp(-j*2*pi*fc*t))

   =1/2A∫exp(-j*2*pi(f-fc)t) + 1/2A ∫exp(-j*2*pi(f+fc)t)dt

   =1/2A(f-fc)+1/2A(f+fc) 
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  • $\begingroup$ this looks like homework. why not just plug into the formula for Fourier transform. $\endgroup$ – thang Feb 27 '15 at 6:34
  • $\begingroup$ what do you mean? :/ yes this is homework. but i should derive the fourier transform of signals. how can I just plug it into fourier formula without deriving it? $\endgroup$ – enver.giourkan Feb 27 '15 at 6:44
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    $\begingroup$ and please learn to use $\LaTeX$ here. put it in between a pair of dollar signs for in-line math and to put an equations out there prominently, put that in between a pair of double dollar signs. for a $\LaTeX$ math reference, i use the one at Wikipedia. $\endgroup$ – robert bristow-johnson Feb 27 '15 at 13:52
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Hey it takes a lot of time in writing equations also I don't know to type in LATEX.so I am sending you image file for second one answer for your second question

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    $\begingroup$ @sagar When someone asks for help with homework, the tradition is to give them help/hints, but not fully solve the problem for them. $\endgroup$ – Jim Clay Feb 27 '15 at 13:11
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    $\begingroup$ @Jim Clay ok sir i will keep it in mind :-) $\endgroup$ – sagar Mar 12 '15 at 15:30

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