3. (20%, Ch5: DFT/FFT)
Let $X(e^{jw})$ denote the DTFT of the sequence $x(n) = (1/2)^n u(n)$. Let $y(n)$ denote a finite-
duration sequence of length 9; i.e., $y(n) = 0, n < 0$, and $y(n) = 0, n \ge 9$. The 9-point DFT
of $y(n)$, denoted by $Y(k)$, corresponds to 9 equally spaced samples of $X(e^{jw})$; i.e.,
$Y(k) = X(e^{j2\pi k/9})$. Please manually determine what is $y(n)$.
Note: this is a manual derivation problem. Use the equation $y(n) = \sum_{r=-\infty}^{\infty} x(n - rN)$
