Suppose you wish to sample an amplitude modulated signal x(t) = m(t) cos( c t) where m(t)

Suppose you wish to sample an amplitude modulated signal x(t) = m(t) cos(Ω_ct) where m(t) is the message signal and Ω_c = 2π10⁴(rad/sec) is the carrier frequency.

(a) If the message is an acoustic signal with frequencies in a band of [0, 22] kHz, what would be maximum frequency present in x(t)?

(b) Determine the range of possible values of the sampling period T_s that would allow to sample x(t) satisfying the Nyquist sampling rate condition.

(c) Given that x(t) is a bandpass signal, compare the above sampling period with the one that can be used to sample bandpass signals.