ASN4 -Fourier Transform property

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[cos(2πf0t)g(t)]=cos(2πf0t)g(t)ej2πftdt

Using Euler's cosine identity cos(2πf0t)g(t)ej2πftdt=12[ej2πf0t+ej2πf0t]g(t)ej2πftdt

cos(2πf0t)g(t)ej2πftdt=12[ej2πf0t+ej2πf0t]g(t)ej2πftdt

[cos(2πf0t)g(t)]=12ej2π(ff0)tg(t)dt+12ej2π(f+f0)tg(t)dt

Identifying that the above equation contains Fourier Transforms the solution is

[cos(2πf0t)g(t)]=12G(ff0)+12[G(f+f0)