# Signal Processing using Fourier Transform

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)

• this looks like homework. why not just plug into the formula for Fourier transform. – thang Feb 27 '15 at 6:34
• 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? – enver.giourkan Feb 27 '15 at 6:44
• 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. – robert bristow-johnson Feb 27 '15 at 13:52