Question

A signal bandlimited to \(5\,\text{kHz}\) must be sampled at a minimum rate of

• A. \(5\,\text{kHz}\)
• B. \(7.5\,\text{kHz}\)
• C. \(10\,\text{kHz}\)
• D. \(20\,\text{kHz}\)

Hint:

The Nyquist sampling rate is \[ \boxed{ f_s \ge 2f_{\max} } \] to avoid aliasing.

Answer 1

The Correct Option is C

Step 1: Apply the Nyquist sampling theorem. According to the Nyquist theorem, \[ f_s \geq 2f_{\max}, \] where \[ f_{\max}=5\,\text{kHz}. \]

Step 2: Calculate the minimum sampling frequency. \[ f_s=2\times5=10\,\text{kHz}. \] Hence, \[ \boxed{10\,\text{kHz}} \] Therefore, \[ \boxed{(C)} \] is the correct answer.