Question

2. An analog signal x(t) = sin(480πt) + 3 sin(720πt) is sampled 600 times per second. (a) Determine the Nyquist sampling rate for x(t). (b) What are the frequencies (in radians) in the resulting discrete time signal xs[n]? (c) If xs[n] is passed through an ideal reconstructor, what is the reconstructed signal y(t)?

Answer 1

Question 2(a)

The analog signal is

This can be written as

So

So the maximum frequency in the signal x(t) is 360 Hz.

Nyquist sampling frequency is twice the maximum frequency. So the Nyquist Sampling Frequency is

So the Nyquist sampling rate is 720 samples per second

Question 2(b)

The signal is sampled with a frequency

So the sampling time period will be

To obtain the sampled signal, we will have to replace t with . So the discrete time signal or the sampled signal will be

So the frequencies in the discrete time signal are