Suppose xe$($r$)$ is a periodic continuous$-$time signal with period $1$ ms and for which the Fourier series is

xe$(1)=$ arel $(20007$ kt$)$

k$=-9$

The Fourier series coefficients ax are zero for $|$K$|>9.$c $($t$)$ is sampled with a sample spacing

T$=$

$10-3$ s to form x $[$n$].$ That is$,$

xInl$=$x$.$

$6000$

$$Is x $[$n$]$ periodic and, if so$,$ with what period?

$$Is the sampling rate above the Nyquist rate? That is$,$ is T sufficiently small to avoid aliasing?

$$Find the DFS coefficients of x $[$n$]$ in terms of ax$.$