Question

Problem 1 I need Problem 2. Thanks Solely based on the formulas $a^n u[n] \rightarrow \frac{1}{1 - az^{-1}}$ and $(n+1) a^n u[n] \rightarrow \frac{1}{(1 - az^{-1})^2}$ determine the $z$-transforms of the following sequences: (a) $x[n] = (n-1)u[n]$ (b) $x[n] = (-1)^n 2^{-n} u[n]$ (c) $x[n] = \cos(\omega_0 n) u[n]$ (d) $x[n] = (nr^n \cos \omega_0 n) u[n]$ (e) $x[n] = Ar^n \sin(\omega_0 n + \phi) u[n]$ Hint: Remember that $\cos$ and $\sin$ yield expressions in terms of complex exponential functions. Problem 2 Given that $\omega_0$, $r$, $A$ are all real, put the $z$-transforms you obtained in Problem 1 in the form of single fractions with only real coefficients. Hint: $a + a^* = 2 \text{Re}(a)$; $a - a^* = 2j \text{Im}(a)$; $\overline{a} = a$; $aa^* = |a|^2$; $(\alpha \beta)^* = \alpha^* \beta^*.$

          Problem 1
I need Problem 2. Thanks
Solely based on the formulas
$a^n u[n] \rightarrow \frac{1}{1 - az^{-1}}$ and $(n+1) a^n u[n] \rightarrow \frac{1}{(1 - az^{-1})^2}$
determine the $z$-transforms of the following sequences:
(a) $x[n] = (n-1)u[n]$
(b) $x[n] = (-1)^n 2^{-n} u[n]$
(c) $x[n] = \cos(\omega_0 n) u[n]$
(d) $x[n] = (nr^n \cos \omega_0 n) u[n]$
(e) $x[n] = Ar^n \sin(\omega_0 n + \phi) u[n]$
Hint: Remember that $\cos$ and $\sin$ yield expressions in terms of complex exponential functions.
Problem 2
Given that $\omega_0$, $r$, $A$ are all real, put the $z$-transforms you obtained in Problem 1 in the form of
single fractions with only real coefficients.
Hint: $a + a^* = 2 \text{Re}(a)$; $a - a^* = 2j \text{Im}(a)$; $\overline{a} = a$; $aa^* = |a|^2$; $(\alpha \beta)^* = \alpha^* \beta^*.$

$Problem 1 I need Problem 2. Thanks Solely based on the formulas a^n u[n] →(1)/(1 - az^-1) and (n+1) a^n u[n] →(1)/((1 - az^-1)^2) determine the z-transforms of the following sequences: (a) x[n] = (n-1)u[n] (b) x[n] = (-1)^n 2^-n u[n] (c) x[n] = cos(ω0 n) u[n] (d) x[n] = (nr^n cosω0 n) u[n] (e) x[n] = Ar^n sin(ω0 n + ϕ) u[n] Hint: Remember that cos and sin yield expressions in terms of complex exponential functions. Problem 2 Given that ω0, r, A are all real, put the z-transforms you obtained in Problem 1 in the form of single fractions with only real coefficients. Hint: a + a^* = 2 Re(a); a - a^* = 2j Im(a); a = a; aa^* = |a|^2; (αβ)^* = α^* β^*.$

Added by Philip C.

Question

Please give Ace some feedback