what is minimum sampling frequency to be satisfied to prevent aliasing if signal frequency is 7.1answer in box must be upto 2 decimal places

1. Break Down the Problem

To determine the minimum sampling frequency required to prevent aliasing, we use the Nyquist-Shannon sampling theorem. According to this theorem, to avoid aliasing, the sampling frequency must be at least twice the highest frequency present in the signal.

2. Relevant Concepts

The formula for the minimum sampling frequency $f_s$ based on the highest frequency $f_{\text{max}}$ is given by: $f_s \geq 2 \cdot f_{\text{max}}$

3. Analysis and Detail

Given:

• Signal frequency $f_{\text{max}} = 7.1 \, \text{Hz}$

We need to calculate the minimum sampling frequency: $f_s \geq 2 \cdot 7.1 \, \text{Hz} = 14.2 \, \text{Hz}$

4. Verify and Summarize

The calculated minimum sampling frequency required to prevent aliasing is $14.2 \, \text{Hz}$.

Final Answer

The minimum sampling frequency to prevent aliasing is: $\boxed{14.20}$