Topic: Electronics Engineering
Determine the DTFT of the sequence $y[n]=(n+1)\alpha^{n}u[n]$ $|\alpha|<1\cdot u[n]$ is unit step sequence
- A. $Y(e^{j\omega})=1/(1-\alpha~e^{-j\omega})^{2}$
- B. $Y(e^{j\omega})=1/(1+\alpha~e^{-j\omega})^{2}$
- C. $Y(e^{j\omega})=\alpha/(1-\alpha~e^{-j\omega})^{2}$
- D. None of these
Answer: A. $Y(e^{j\omega})=1/(1-\alpha~e^{-j\omega})^{2}$
Explanation: $y(n)=(n+1)\alpha^{n}u(n),\alpha<1$
$y(n)=n\alpha^{n}u(n)+\alpha^{n}u(n)$
$Y(e^{j\omega})=\frac{\alpha e^{-j\omega}}{(1-\alpha e^{-j\omega})^{2}}+\frac{1}{1-\alpha e^{-j\omega}} = \frac{1}{(1-\alpha e^{-j\omega})^{2}}$