Signals — And Systems Problems And Solutions Pdf Free

\subsection*Problem 8: Z-Transform of a Causal Sequence Find the Z-transform and ROC of \(x[n] = (0.5)^n u[n] + (2)^n u[-n-1]\).

\subsection*Solution Even part: \(x_e(t) = \fracx(t) + x(-t)2 = \frace^-atu(t) + e^atu(-t)2\). \\ Odd part: \(x_o(t) = \fracx(t) - x(-t)2 = \frace^-atu(t) - e^atu(-t)2\). signals and systems problems and solutions pdf

\noindent\textbf14. Z-transform of \(x[n]=n(1/3)^n u[n]\). \textitAns: \(\frac(1/3)z^-1(1-(1/3)z^-1)^2\), \(|z|>1/3\). \subsection*Problem 8: Z-Transform of a Causal Sequence Find