A message m(t) with a bandwidth of B = 2 kHz modulates a cosine carrier of frequency 10 kHz to obtain a modulated signal s(t) = m(t)cos(20 × 10³πt).

(a) What is the maximum frequency of s(t)? What would be the values of the sampling frequency f_s in Hz, according to the Nyquist sampling condition, that could be used to sample s(t)?

(b) Assume the spectrum of m(t) is a triangle, with maximum amplitude 1, carefully plot the spectrum of s(t). Would it be possible to sample s(t) with a sampling frequency f_s = 10 kHz and recover the original message? Obtain the spectrum of the sampled signal and show how you would recover m(t), if possible.