Signals And Systems Problems And Solutions Pdf Review

\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.

\noindent\textbf14. Z-transform of \(x[n]=n(1/3)^n u[n]\). \textitAns: \(\frac(1/3)z^-1(1-(1/3)z^-1)^2\), \(|z|>1/3\). signals and systems problems and solutions pdf

\titleSignals and Systems: \\ Problems and Solutions \authorStudy Guide \date\today but for time-invariance we need \(x(t-\tau)\cos(t-\tau)\).

\subsection*Problem 9: Nyquist Rate A signal \(x(t) = \textsinc(100t) + \textsinc^2(50t)\). Find the Nyquist sampling rate. signals and systems problems and solutions pdf

\noindent\textbf15. Is \(y(t)=x(t)\cos(t)\) LTI? \textitAns: No, time-varying.

\subsection*Problem 7: Region of Convergence Find the Laplace transform and ROC of \(x(t) = e^-2tu(t) + e^3tu(-t)\).

\noindent\textbf15. Check: Input \(x(t-\tau)\) gives \(x(t-\tau)\cos t\), but for time-invariance we need \(x(t-\tau)\cos(t-\tau)\).