Sampling

The discrete-time sinusoidal signal

$$x[n] = 3 \cos(2\pi 0.3 n + \frac{\pi}{4}).$$

is obtained by sampling a continuous-time sinusoid of the form

$$x(t) = A \cos(2\pi f t + \phi)$$

at rate f_s=8000 Hz.

1.

Provide three different sets of paramters A, f, and $\phi$ for the continuous-time sinusoid that all yield the discrete-time sinusoid above when sampled at the indicated rate. The parameter f must satisfy 0<f<12000 Hz in all three cases.

2.

For each case indicate if the signal is undersampled or oversampled and if aliasing or folding occurred.