An analog input signal x(t) = 1.5 + 1.5sin(5t) is sampled with 1 kHz sampling frequency fs. Assuming that sampling starts at t = 0 compute the value of the sample x[6]:
To compute the value of the sample x[6], we use the formula for sampling:
x[n] = x(nT), where T = 1/fs is the sampling period.
In this case, fs = 1 kHz, so T = 1/1000 sec.
To get x[6], we use n = 6:
x[6] = x(6T)
= x(6/1000) (since T = 1/1000 sec)
= 1.5 + 1.5sin(5(6/1000))
= 1.5 + 1.5sin(0.03)
= 1.5 + 1.5(0.02999)
= 1.545
Therefore, the value of the sample x[6] is 1.545.