what is minimum sampling frequency to be satisfied to prevent aliasing if signal frequency is 8.7answer in box must be upto 2 decimal places

1. Break Down the Problem

To prevent aliasing, we need to determine the minimum sampling frequency using the Nyquist theorem. The Nyquist theorem states that the sampling frequency must be at least twice the maximum frequency of the signal.

2. Relevant Concepts

The formula for the minimum sampling frequency $f_s$ is given by: $f_s \geq 2 \times f_{max}$ where $f_{max}$ is the maximum frequency of the signal.

3. Analysis and Detail

Given the signal frequency $f_{max} = 8.7 \, \text{Hz}$, we can calculate the minimum sampling frequency as: $f_s \geq 2 \times 8.7 = 17.4 \, \text{Hz}$

4. Verify and Summarize

The calculations show that to prevent aliasing for a signal frequency of 8.7 Hz, the minimum sampling frequency must be 17.4 Hz.

Final Answer

$\boxed{17.40}$