How can I derive the fourier transform of
g1(t) = {A cos(2πfc t),−T/2 < t 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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