Signals And Systems Problems And: Solutions Pdf
\noindent\textbf15. Check: Input \(x(t-\tau)\) gives \(x(t-\tau)\cos t\), but for time-invariance we need \(x(t-\tau)\cos(t-\tau)\).
\titleSignals and Systems: \\ Problems and Solutions \authorStudy Guide \date\today
\noindent\textbf15. Is \(y(t)=x(t)\cos(t)\) LTI? \textitAns: No, time-varying. signals and systems problems and solutions pdf
\noindent\textbf11. Compute convolution of \(x[n]=u[n]-u[n-3]\) and \(h[n]=u[n]-u[n-2]\). \\ \textitAns: \(y[n]=[1,2,2,1]\) for \(n=0..3\).
\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: \(-2 < \textRe(s) < 3\). \noindent\textbf15
\subsection*Problem 2: Even and Odd Decomposition Find the even and odd parts of \(x(t) = e^-atu(t)\), where \(u(t)\) is the unit step.
\subsection*Problem 9: Nyquist Rate A signal \(x(t) = \textsinc(100t) + \textsinc^2(50t)\). Find the Nyquist sampling rate. ROC: \(-2 <
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