Question

1. Given the following sequence: $f[n] = 2^n u[n]$. (a) (16 points) Determine whether $f[n]$ is absolutely summable. (b) (16 points) Determine whether the Fourier transform of $f[n]$ converges and why. (c) (20 points) Let $y[n] = a^{-1}f[n]$, for what values of $a$ does the Fourier transform of $y[n]$ converge? (d) (16 points) By the definition of z-transform, obtain the z-transform $F(z)$ of $f[n]$ and its region of convergence (ROC). (e) (12 points) What is the difference between the regions of convergence in (c) and (d)? Comment elaborately. (f) (20 points) Given that $F(z)$ where $z = 3e^{j\Omega}$, is the Fourier transform of a sequence $f_1[n]$, then obtain $f_1[n]$.

          1. Given the following sequence:
$f[n] = 2^n u[n]$.
(a) (16 points) Determine whether $f[n]$ is absolutely summable.
(b) (16 points) Determine whether the Fourier transform of $f[n]$ converges and why.
(c) (20 points) Let $y[n] = a^{-1}f[n]$, for what values of $a$ does the Fourier transform of $y[n]$ converge?
(d) (16 points) By the definition of z-transform, obtain the z-transform $F(z)$ of $f[n]$ and its region of convergence (ROC).
(e) (12 points) What is the difference between the regions of convergence in (c) and (d)? Comment elaborately.
(f) (20 points) Given that $F(z)$ where $z = 3e^{j\Omega}$, is the Fourier transform of a sequence $f_1[n]$, then obtain $f_1[n]$.

1 given the following sequence fn 2n un a 16 points determine whether fn is absolutely summable b 16 points determine whether the fourier transform of fn converges and why c 20 points let yn 71444

Added by Carmen S.

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