Sampling

Let $x(t) = 3\cos(2\pi550t + \pi/4)$. In each of the following parts, the discrete-time signal x[n] is obtained by sampling x(t) at rate f_s. Then, the resulting x[n] can be written as:

$$x[n] = A \cos(2\pi\hat{f}n + \phi).$$

For each part below, determine the values of A, $\hat{f}$ (the digital frequency $\hat{f}$ in your answer must satisfy $0 \leq \hat{f} \leq 0.5$), and $\phi$.

1.

Let the sampling frequency be f_s=100 Hz.

2.

Let the sampling frequency be f_s=1000 Hz.

3.

Let the sampling frequency be f_s=10000 Hz.