Signals And Systems Problems And Solutions Pdf -
\subsection*Problem 4: Trigonometric Fourier Series Find the Fourier series of the periodic square wave \(x(t)\) with period \(T=2\), defined on \((-1,1)\) as \(x(t)=1\) for \(|t|<0.5\) and \(x(t)=0\) otherwise.
\sectionSampling and Aliasing
\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
\subsection*Solution Modulation: \(x(t)\cos(\omega_0 t) \leftrightarrow \frac12[X(j(\omega-\omega_0)) + X(j(\omega+\omega_0))]\). \\ Thus \(\textrect(t/T)\cos(\omega_0 t) \leftrightarrow \fracT2\left[\textsinc\left(\frac(\omega-\omega_0)T2\pi\right) + \textsinc\left(\frac(\omega+\omega_0)T2\pi\right)\right]\).
\noindent\textbf15. Is \(y(t)=x(t)\cos(t)\) LTI? \textitAns: No, time-varying. defined on \((-1
\noindent\textbf11. \(x[n]=\delta[n]+\delta[n-1]+\delta[n-2]\), \(h[n]=\delta[n]+\delta[n-1]\). Convolution gives \(y[n]=\delta[n]+2\delta[n-1]+2\delta[n-2]+\delta[n-3]\).
\titleSignals and Systems: \\ Problems and Solutions \authorStudy Guide \date\today 1)\) as \(x(t)=1\) for \(|t|<
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