Problem $10\mathrm{.}049$

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Each signal$$ x below is sampled to form xs $$by being multiplied by a periodic impulse of the form$$Ts$($t$)$ for continuous$-$time signals or$$Ns$[$n$]$for discrete$-$time signals and fs $=1/$Ts$$and Ns $=1/$Fs $.$

$$

Problem $10\mathrm{.}049.$b$-$Impulse Sampling

The signal x$[$n$]$ and the sampling interval Ns is given by

$$

x$[$n$]=3$sin$(2$n$10)$x$[$n$]=3$sin$(2$n$10)$

$$

Ns$=4$Ns$=4$

$$

If the sampled signal is filtered by an ideal lowpass discrete$-$time filter, what is the maximum corner frequency that would produce a pure sinusoidal response from the filter?

What is the maximum corner frequency that would produce no response at all from the filter?

The maximum corner frequency that would produce a pure sinusoidal response from the filter is Hz$.$

The maximum corner frequency that would produce no response at all from the filter is Hz$.$