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Question 1 (8 marks) Consider a continuous time periodic signal y(t) = 6 \cos(23\pi t) + 3 \sin(16\pi t) (a) State the Nyquist sampling rate of y(t). (b) Regardless of your answer in (a), assume sampling frequency $f_s = 5$Hz. Write down the sampled data y[n] for n = 0, 1,..., 9. Suppose y[0] = y(0). (Give your answers correct to two decimal places) (c) Consider the following quantizer $\begin{aligned} Q(x) = \begin{cases} 6, & x \ge 4\\ 2, & 0 \le x < 4\\ 0, & -4 \le x < 0\\ -2, & -4 \le x < 0\\ -6, & x < -4 \end{cases} \end{aligned}$ Write down the quantized samples v[n] = Q(y[n]) (d) Compute the quantization error q[n] = v[n] - y[n]. (e) Under the conditions set above, determine the length of bit stream required to store y(t) for 8 seconds.

          Question 1 (8 marks)
Consider a continuous time periodic signal
y(t) = 6 \cos(23\pi t) + 3 \sin(16\pi t)
(a) State the Nyquist sampling rate of y(t).
(b) Regardless of your answer in (a), assume sampling frequency $f_s = 5$Hz. Write down the sampled data y[n] for n = 0, 1,..., 9. Suppose y[0] = y(0). (Give your answers correct to two decimal places)
(c) Consider the following quantizer
$\begin{aligned} Q(x) = \begin{cases} 6, & x \ge 4\\ 2, & 0 \le x < 4\\ 0, & -4 \le x < 0\\ -2, & -4 \le x < 0\\ -6, & x < -4 \end{cases} \end{aligned}$
Write down the quantized samples v[n] = Q(y[n])
(d) Compute the quantization error q[n] = v[n] - y[n].
(e) Under the conditions set above, determine the length of bit stream required to store y(t) for 8 seconds.

Question 1 (8 marks)
Consider a continuous time periodic signal
y(t) = 6 cos(23πt) + 3 sin(16πt)
(a) State the Nyquist sampling rate of y(t).
(b) Regardless of your answer in (a), assume sampling frequency fs = 5Hz. Write down the sampled data y[n] for n = 0, 1,..., 9. Suppose y[0] = y(0). (Give your answers correct to two decimal places)
(c) Consider the following quantizer
Q(x) = 6, x ≥ 4
2, 0 ≤ x < 4
0, -4 ≤ x < 0
-2, -4 ≤ x < 0
-6, x < -4
Write down the quantized samples v[n] = Q(y[n])
(d) Compute the quantization error q[n] = v[n] - y[n].
(e) Under the conditions set above, determine the length of bit stream required to store y(t) for 8 seconds.

Added by Stacey K.

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