1.

If x(n)=A, -M

Answer»

Right option is (c) A\(\FRAC{sin⁡(M+\frac{1}{2})ω}{sin⁡(\frac{ω}{2})}\)

For explanation: CLEARLY, x(n)=x(-n). THUS the signal x(n) is real and even signal. So, we know that

\(X(ω)=X_R(ω)=A(1+2∑_{n=1}^∞ cos⁡ωn)\)

On simplifying the above equation, we obtain

X(ω)=A\(\frac{sin⁡(M+\frac{1}{2})ω}{sin⁡(\frac{ω}{2})}\).


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