How many minimum number of samples are required to exactly describe the following signal?

x(t) = 10 cos(6πt) + 4 sin(8πt)

Sampling Theorem:

 A continuous-time signal can be represented in its samples and can be recovered back when sampling frequency (f_s)is greater than or equal to twice the highest frequency component of the message signal (f_m).

The sampling frequency is given by:

\(f_s=2\times max(f_{m1},f_{m2})\)

Calculation:

Given, x(t) = 10 cos(6πt) + 4 sin(8πt)

6π = 2πf_m1

f_m1 = 3 Hz

8π = 2πfm2

fm2 = 4 Hz

\(f_s=2\times max(3,4)\)

f_s = 8 Hz

fs = 8 samples per second