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Find ℱ[cos(2πf0t)g(t)]
Recall w0=2πf0, so
Using Euler's cosine identity ∫−∞∞cos(2πf0t)g(t)e−j2πftdt=∫−∞∞12[ej2πf0t+e−j2πf0t]g(t)e−j2πftdt
Now ℱ[cos(2πf0t)g(t)]=12∫−∞∞e−j2π(f−f0)tg(t)dt+12∫−∞∞e−j2π(f+f0)tg(t)dt
So ℱ[cos(2πf0t)g(t)]=12[G(f−f0)+G(f+f0)]