Question

Suppose you wish to sample an amplitude modulated signal x(t)-m(t) cos(Q,t) where m(1) is the message signal and Ω,-2π 10 (rad/sec) is the carrier frequency 8.6 a) If the message is anacusic signal with frequencies in a band of [0, 22] kHz, what would be maximum frequency present in x(t)?

Answer 1

Maximum frequency is 32 Khz.

Consider the given modulated signal: x (t) = m (t) cos (ohm_c t) where m (t) is message signal in frequency range [0, 22] KHz Let us assume that the Fourier Transform of message signal m (t) is as follow: Note that we don't know the exact shape of n (f) for sure. But we are sure that the maximum frequency of M (f) is 22 KHz and minimum is 0 KHz. Therefore such assumption for M (f) is valid for finding frequency of the modulated wave. Now, we know that the Fourier Transform of x (t) which is multiplication of m (t) and cos (2 pi 10^4 t) is given as follow: \r\n Now, frequency of carrier X (f) signal is: f_c = ohm_c/2 pi = 2 pi 10^4/2 pi = 10^4 Hz = 10 KHz we know that 10^4 Hz = 10 KHz Therefore the Fourier Transform of X (f) is: Therefore Maximum frequency present in x (t)