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\noindent\textbf14. Z-transform of \(x[n]=n(1/3)^n u[n]\). \textitAns: \(\frac(1/3)z^-1(1-(1/3)z^-1)^2\), \(|z|>1/3\).
\documentclass[12pt,a4paper]article \usepackage[utf8]inputenc \usepackageamsmath, amssymb, amsthm \usepackagegraphicx \usepackagehyperref \usepackagegeometry \geometrymargin=1in \usepackagetitlesec \titleformat\section\large\bfseries\thesection1em{} signals and systems problems and solutions pdf
\subsection*Solution \(y(t) = \int_-\infty^\infty e^-\tauu(\tau) \cdot [u(t-\tau) - u(t-\tau-2)] d\tau\). For \(t < 0\): \(y(t)=0\). For \(0 \le t < 2\): \(y(t) = \int_0^t e^-\tau d\tau = 1 - e^-t\). For \(t \ge 2\): \(y(t) = \int_t-2^t e^-\tau d\tau = e^-(t-2) - e^-t\). Thus \[ y(t) = \begincases 0, & t<0 \\ 1-e^-t, & 0\le t < 2 \\ e^-(t-2) - e^-t, & t \ge 2 \endcases \] \noindent\textbf14
\section*Additional Problems (Brief Solutions) a4paper]article \usepackage[utf8]inputenc \usepackageamsmath
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\noindent\textbf15. Is \(y(t)=x(t)\cos(t)\) LTI? \textitAns: No, time-varying.
\section*Solutions to Selected Additional Problems