Question

An analog voltage signal is given by V(t) = 3 + cos(2πt) + 4cos(4πt) + 2cos(6πt). Suppose the given analog signal is recorded in a digital form through a digital data acquisition system. The system samples the signal discretely at a sampling frequency of 10Hz. Is the sampling frequency appropriate to avoid aliasing issue?

Answer 1

The sampling frequency of 10 Hz is appropriate to avoid aliasing in this digital data acquisition system.

Step-by-step explanation:

The given analog signal can be expressed as V(t) = 3 + cos(2πt) + 4cos(4πt) + 2cos(6πt). To avoid aliasing, the Nyquist-Shannon sampling theorem states that the sampling frequency should be at least twice the highest frequency component of the analog signal. In this case, the highest frequency component is 6π = 18.85 Hz. Therefore, the sampling frequency of 10 Hz is appropriate to avoid aliasing since it is greater than 2 * 18.85 Hz.