7. (CLO7) Sampling
Suppose $X_r(j\omega) = \delta(\omega - 6) + \delta(\omega + 6)$
A. Sketch $X_r(j\omega)$
B. What is $\omega_0$? Hint: See the FT pairs table on the help sheet.
C. What is the Nyquist rate for this signal?
$\omega_N = ____$
$f_N = ____$
D. Suppose we sample at $f_s = 5$ Hz. Sketch the spectrum and label the
axes.
E. To reconstruct the original signal, we need to low-pass filter to remove
the replicas. For an ideal LPF, what range of cutoff frequencies will
reconstruct the signal?
$____ < \omega_c < ____$
F. What should be the gain (magnitude) in the passband, for ideal
reconstruction?