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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.

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.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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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.)
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.)
### Mathematical Transcriptions #### Part d) The given function is expressed as: \[ \hat{G}(z) = \left(\frac{3}{8}\right) \frac{z^{-1} e^{-j0.35\pi}}{z e^{-j0.35\pi} - 1} + \left(\frac{3}{8}\right) \frac{z^{-1} e^{j0.35\pi}}{z e^{j0.35\pi} - 1} \] This represents a complex-valued function in the z-domain involving exponential and trigonometric terms. #### Part e) The given function is expressed as: \[ \hat{Y}(z) = \frac{15/j}{z + 0.25\sqrt{2} - j0.25\sqrt{2}} - \frac{15/j}{z + 0.25\sqrt{2} + j0.25\sqrt{2}} - \frac{4}{z-1} + \frac{5}{z-0.16} \] This formula involves summation and subtraction of several rational expressions in the z-domain, with complex numbers present in the denominators.
Transcribed Image Text:### Mathematical Transcriptions #### Part d) The given function is expressed as: \[ \hat{G}(z) = \left(\frac{3}{8}\right) \frac{z^{-1} e^{-j0.35\pi}}{z e^{-j0.35\pi} - 1} + \left(\frac{3}{8}\right) \frac{z^{-1} e^{j0.35\pi}}{z e^{j0.35\pi} - 1} \] This represents a complex-valued function in the z-domain involving exponential and trigonometric terms. #### Part e) The given function is expressed as: \[ \hat{Y}(z) = \frac{15/j}{z + 0.25\sqrt{2} - j0.25\sqrt{2}} - \frac{15/j}{z + 0.25\sqrt{2} + j0.25\sqrt{2}} - \frac{4}{z-1} + \frac{5}{z-0.16} \] This formula involves summation and subtraction of several rational expressions in the z-domain, with complex numbers present in the denominators.
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