Solution to Q5 of Week 5 Quiz Pool
By Nyquist condition, the sampling frequency must be larger than the twice of maximum signal frequency, in order to avoid the aliasing when sampling.
$ \begin{align} x(t) &= \text{cos}(1000 \pi t) + \text{sin}(1500 \pi t) \\ &= \text{cos}(2\pi \times 500 t) + \text{sin}(2\pi \times 750 t) \end{align} \,\! $
Thus, it consists of two sinusoidal with frequencies equal to 500 Hz and 750 Hz, respectively.
Since the maximum frequency is 750 Hz, the sampling frequency must be greater than 1500 Hz, which is
$ F_s > 2\times 750 = 1500 \text{ Hz} \,\! $
Solution to Q6 of Week 5 Quiz Pool
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