Signals And Systems Problems And Solutions Pdf | EXTENDED ✧ |

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\subsection*Problem 3: Convolution Integral Given \(x(t) = e^-tu(t)\) and \(h(t) = u(t) - u(t-2)\), compute \(y(t) = x(t) * h(t)\). signals and systems problems and solutions pdf

\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: \(-2 < \textRe(s) < 3\). a4paper]article \usepackage[utf8]inputenc \usepackageamsmath

\subsection*Problem 5: Fourier Transform of a Rectangular Pulse Compute the Fourier transform of \(x(t) = \textrect(t/T) = 1\) for \(|t| < T/2\), 0 otherwise. ROC: \(-2 &lt