\section*Conclusion This document provides a solid foundation in signals and systems problem-solving. Further study should include MATLAB/Python simulations and more advanced topics like state-space representation and filter design.
\subsection*Problem 1: Signal Energy and Power For the signal \( x(t) = A \cos(2\pi f_0 t + \theta) \), determine whether it is an energy signal or a power signal. Compute its average power. signals and systems problems and solutions pdf
\subsection*Problem 9: Nyquist Rate A signal \(x(t) = \textsinc(100t) + \textsinc^2(50t)\). Find the Nyquist sampling rate. 0.5\). \\ Second term: \(-\frac11-2z^-1\)
\subsection*Solution First term: \(\frac11-0.5z^-1\), \(|z| > 0.5\). \\ Second term: \(-\frac11-2z^-1\), \(|z| < 2\). \\ Thus \(X(z) = \frac11-0.5z^-1 - \frac11-2z^-1 = \frac-1.5z^-1(1-0.5z^-1)(1-2z^-1)\), ROC: \(0.5 < |z| < 2\). ROC: \(0.5 <
\sectionZ-Transform (Discrete-Time)
\noindent\textbf14. Z-transform of \(x[n]=n(1/3)^n u[n]\). \textitAns: \(\frac(1/3)z^-1(1-(1/3)z^-1)^2\), \(|z|>1/3\).