BC:6.2 Use the z-transform tables of one-sided z-transform tranform pairs and properties to determine the (causal) sampled time function for each of the following z-domain functions. Assume a Region of Convergence of |z|> 1 is sufficient for the one-sided z-transform. a.) b.) F(z): Ĥ(z) = - 52² - 13z + 17 232² 2 -1252-2 2² +0.5z 23-0.1522 X(z) = 1326 + +3 27 +0.826

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**BC:6.2** Use the z-transform tables of one-sided z-transform transform pairs and properties to determine the (causal) sampled time function for each of the following z-domain functions. Assume a Region of Convergence of \(|z| > 1\) is sufficient for the one-sided z-transform.

a.)  
\[
\hat{F}(z) = \frac{5z^2 - 13z + 17}{z^5}
\]

b.)  
\[
\hat{H}(z) = \frac{-125z^{-2}}{z^2 + 0.5z} + \frac{23z^2}{z^3 - 0.15z^2}
\]

c.)  
\[
\hat{X}(z) = \frac{13z^6 - 7z^4 + 3}{z^7 + 0.8z^6}
\]

d.)  
\[
\hat{G}(z) = \left(\frac{3}{8}\right)\frac{z^{-1}e^{-j0.35\pi}}{ze^{-j0.35\pi} - 1} + \left(\frac{3}{8}\right)\frac{z^{-1}e^{j0.35\pi}}{ze^{j0.35\pi} - 1}
\]

e.)  
\[
\hat{Y}(z) = \frac{15/j}{z + 0.25\sqrt{2} - j0.25\sqrt{2}} - \frac{15/j}{z + 0.25\sqrt{2} + j0.25\sqrt{2}} - \frac{4}{z - 1} + \frac{5}{z - 0.16}
\]
Transcribed Image Text:**BC:6.2** Use the z-transform tables of one-sided z-transform transform pairs and properties to determine the (causal) sampled time function for each of the following z-domain functions. Assume a Region of Convergence of \(|z| > 1\) is sufficient for the one-sided z-transform. a.) \[ \hat{F}(z) = \frac{5z^2 - 13z + 17}{z^5} \] b.) \[ \hat{H}(z) = \frac{-125z^{-2}}{z^2 + 0.5z} + \frac{23z^2}{z^3 - 0.15z^2} \] c.) \[ \hat{X}(z) = \frac{13z^6 - 7z^4 + 3}{z^7 + 0.8z^6} \] d.) \[ \hat{G}(z) = \left(\frac{3}{8}\right)\frac{z^{-1}e^{-j0.35\pi}}{ze^{-j0.35\pi} - 1} + \left(\frac{3}{8}\right)\frac{z^{-1}e^{j0.35\pi}}{ze^{j0.35\pi} - 1} \] e.) \[ \hat{Y}(z) = \frac{15/j}{z + 0.25\sqrt{2} - j0.25\sqrt{2}} - \frac{15/j}{z + 0.25\sqrt{2} + j0.25\sqrt{2}} - \frac{4}{z - 1} + \frac{5}{z - 0.16} \]
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