modulation.tex
No OneTemporary
Actions

Subscribers

None

File Metadata

	\begin{exercise}{(15 points)}
	Consider the real-valued signal $x[n]$ whose DTFT is sketched (in magnitude) here:

	\begin{center}
	\begin{dspPlot}[height=3cm,xtype=freq,xticks=4,yticks=none]{-1,1}{0, 1.5}
	% \pnode(0,0){o} \pnode(\wc,0){a} \pnode(-\wc,0){b}
	\dspFunc{x \dspTri{0.25}{.125} x \dspTri{-0.25}{.125} add}
	\dspCustomTicks[axis=x]{0.125 $\pi/8$}
	\end{dspPlot}
	\end{center}

	Sketch as accurately as possible the magnitude of the spectrum of the following signals:
	\begin{enumerate}
	\item $y_1[n] = x[n]\cos(\omega_1 n), \quad$ with $\omega_1 = \pi/4$
	\item $y_2[n] = x[n]\cos(\omega_2 n), \quad$ with $\omega_2 = 11\pi/16$
	\end{enumerate}
	\end{exercise}



	\begin{exercise}{(20 points)}
	Consider a signal $x[n]$ with the following (real-valued) spectrum:
	\begin{center}
	\begin{dspPlot}[height=3cm,xtype=freq,xticks=4,yticks=1,ylabel={$X(e^{j\omega})$},xout=true]{-1,1}{0,1.1}
	\dspFunc{x \dspTri{0}{.25}}
	\end{dspPlot}
	\end{center}

	Sketch \emph{as accurately as possible} the spectrum of the following signals:
	\begin{enumerate}
	\item $a[n] = x[n]\,(1+\cos((\pi/4)n))$
	\item $b[n] = x[n]\,\cos((7\pi/8)n)$
	\end{enumerate}
	\end{exercise}