a$.$ Determine and simplify the discrete$-$time signal $x(n)$ obtained by uniformly sampling at a sampling rate of $500$ Hz a continuous$-$time signal $x(t)$ given below.

$x(t)=3cos(2300t)+2sin(2600t)-sin(2900t)$

b$.$ Let's use an ideal $\frac{D}{A}$ converter to reconstruct the continuous$-$time signal from $x(n).$ Find the reconstructed signal $y(t)$ from $x(n).$

$(5$ points$)$

c$.$ Determine the minimum required number of bits per sample and quantized signal frequency for minimum SQNR $60$dB

$(5$ points$)$

d$.$ If the signal has $x_{\text{m}\text{a}\text{x}}=3V$ and $x_{\text{m}\text{i}\text{n}}=-3V,$ what is the resolution $$ for $($c$)$

$(5$ points$)$