Question

Write a MATLAB program that will generate and plot two periods of the continuous-time signal I I . Use a time interval of 0.1 ms. Laboratory Work 1. Determine the minimum sampling frequency necessary for the signal to be unambiguously represented by the samples.

Answer 1

The minimum sampling frequency necessary for the continuous-time signal to be unambiguously represented by the samples is 20 kHz.

Step-by-step explanation:

To determine the minimum sampling frequency necessary for the continuous-time signal to be unambiguously represented by the samples, we need to consider the Nyquist-Shannon sampling theorem. According to this theorem, the sampling frequency should be at least twice the maximum frequency component present in the continuous-time signal.

Since the continuous-time signal has two periods, the maximum frequency component can be determined as the reciprocal of the minimum time period between the samples. In this case, the time interval between the samples is given as 0.1 ms. Therefore, the maximum frequency component is 1 / 0.1 ms = 10 kHz.

Based on the Nyquist-Shannon sampling theorem, the minimum sampling frequency required to unambiguously represent the continuous-time signal is 2 times the maximum frequency component, which is 2 × 10 kHz = 20 kHz.