If x(n)=cosω0n and W(ω) is the Fourier transform of the rectangular signal w(n), then what is the Fourier transform of the signal x(n).w(n)?
A. 1/2[W(ω-ω0)- W(ω+ω0)].
B. 1/2[W(ω-ω0)+ W(ω+ω0)].
C. [W(ω-ω0)+ W(ω+ω0)].
D. [W(ω-ω0)- W(ω+ω0)].
Answer:A
If x(n)=cosω0n and W(ω) is the Fourier transform of the rectangular signal w(n), then what is the Fourier transform of the signal x(n).w(n)?
A. 1/2[W(ω-ω0)- W(ω+ω0)]. B. 1/2[W(ω-ω0)+ W(ω+ω0)]. C. [W(ω-ω0)+ W(ω+ω0)]. D. [W(ω-ω0)- W(ω+ω0)].
Explanation: According to the exponential properties of Fourier transform, we get