Question

4. Use the multiplication property of the Discrete Fourier Transform (DTFT) to find the Fourier transform of the amplitude modulated discrete time signal r[n] = s[n]p[n] where the information signal is s[n] = \frac{12\sin(\frac{\pi n}{10})}{\pi n} and the carrier signal p[n] = \cos(\frac{\pi n}{2}). Plot the graph of R(e^{j\omega}) in the interval $-3\pi \le \omega \le 3\pi$. \textbullet Using MATLAB, sketch and label the magnitude of the Fourier transform R(e^{j\omega}) for the interval $-3\pi \le \omega \le 3\pi$ and compare it with your sketch from the mathematical result (plot the final result as a function of $\omega/\pi$). You need to provide your MATLAB codes for the plot and the results.

          4. Use the multiplication property of the Discrete Fourier Transform (DTFT) to
find the Fourier transform of the amplitude modulated discrete time signal
r[n] = s[n]p[n] where the information signal is s[n] = \frac{12\sin(\frac{\pi n}{10})}{\pi n} and the carrier
signal p[n] = \cos(\frac{\pi n}{2}). Plot the graph of R(e^{j\omega}) in the interval $-3\pi \le \omega \le 3\pi$.
\textbullet Using MATLAB, sketch and label the magnitude of the Fourier transform
R(e^{j\omega}) for the interval $-3\pi \le \omega \le 3\pi$ and compare it with your sketch from
the mathematical result (plot the final result as a function of $\omega/\pi$). You need
to provide your MATLAB codes for the plot and the results.

4. Use the multiplication property of the Discrete Fourier Transform (DTFT) to
find the Fourier transform of the amplitude modulated discrete time signal
r[n] = s[n]p[n] where the information signal is s[n] = (12sin((πn)/(10)))/(πn) and the carrier
signal p[n] = cos((πn)/(2)). Plot the graph of R(e^jω) in the interval -3π≤ω≤ 3π.
•Using MATLAB, sketch and label the magnitude of the Fourier transform
R(e^jω) for the interval -3π≤ω≤ 3π and compare it with your sketch from
the mathematical result (plot the final result as a function of ω/π). You need
to provide your MATLAB codes for the plot and the results.

Added by Ignacio B.

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