Question

Problem 6 10 Points Your system samples a sinusoidal signal (t) cos(2T800t) with f 600 samples per second. After sampling, the reconstructed signal appears as a sinusoid at what frequency in Hertz?

Answer 1

Sampling theorem as sigma^infinity_n = -infinity n (t - n T_s) = 1/T_s sigma^infinity_n = -infinity times (t - n/T_s) 1/T_s = f_s f_s is sampling frequency To avoid f_s greaterthanorequalto 2f [where f i.e. max frequence of x (t)] x (t) = cos (2 pi 800t) x (t) = 1/2 [delta (f - 800) + delta (f + 800)] x_s (f) = 1/T_S sigma^infinity_n = -infinity times (f - n/T_s) x_s (f) = f_s sigma^infinity_n = -infinity times (f - nf_s) x_s (f) = [600] { + x (f + f_s) + x (f) + x (f - f_s) +..] \r\n x_s (t) = 300 [+ ..+ s (f - 200) + s (f + 200) + s (f - 400) + s (f + 400) + s (f - 800) + s (f + 800) + s (f - 1000) + s (f + 1000) +..] x_s (t) = 600 [+ .. + cos (2 pi 200t) + cos (2 pi 400t) + + cos (2 pi 800t)