Signals And Systems Problems And Solutions Pdf -

\titleSignals and Systems: \\ Problems and Solutions \authorStudy Guide \date\today

\subsection*Solution First term: \(e^-2tu(t) \leftrightarrow \frac1s+2\), \(\textRe(s) > -2\). \\ Second term: \(e^3tu(-t) \leftrightarrow -\frac1s-3\), \(\textRe(s) < 3\). \\ Thus \(X(s) = \frac1s+2 - \frac1s-3 = \frac-5(s+2)(s-3)\), ROC: \(-2 < \textRe(s) < 3\). signals and systems problems and solutions pdf

\subsection*Solution Stability: \(\int_-\infty^\infty |h(t)| dt = \int_-\infty^\infty e^- dt = 2\int_0^\infty e^-t dt = 2\). Finite ⇒ stable. \\ Causality: \(h(t) \neq 0\) for \(t<0\) ⇒ not causal. ROC: \(-2 &lt

\noindent\textbf11. \(x[n]=\delta[n]+\delta[n-1]+\delta[n-2]\), \(h[n]=\delta[n]+\delta[n-1]\). Convolution gives \(y[n]=\delta[n]+2\delta[n-1]+2\delta[n-2]+\delta[n-3]\). signals and systems problems and solutions pdf