Question $1(10$ marks$)$

Consider a continuous time periodic signal

$y(t)=8cos(24t)+4sin(18t)$

$($a$)$ State the Nyquist sampling rate of $y(t).$

$($b$)$ Assume sampling frequency $f_s=40Hz.$ Write down the sampled data $y[n]$ for $n=0,1,$dots,$8.$ Suppose $y[0]=y(0).($Give your answers correct to $3$ decimal places$)$

$($c$)$ Consider the following quantizer

Write down the quantized samples $v[n]=Q(y[n])$

$($d$)$ Compute the quantization error $q[n]=v[n]-y[n].$

$($e$)$ What is the length of bit stream required to store $y(t)$ for $6$ seconds?