How frequently must an analog signal be sampled to be accurately reproduced?
The correct answer is B: At least twice the rate of the highest frequency component of the signal. How frequently must an analog signal be sampled to be accurately reproduced is at least twice the rate of the highest frequency component of the signal. This is the Nyquist sampling theorem. For amateur radio operators, this is important for digital signal processing. Understanding this helps when working with ADCs.
Exam Tip
Sampling frequency for accurate reproduction = at least twice the highest frequency component. Think 'N'yquist = 'N'eed '2'× highest frequency. This is the Nyquist sampling theorem. Not half, not same rate, not four times - just at least twice.
Memory Aid
"Sampling frequency for accurate reproduction = at least twice the highest frequency component. Think 'N'yquist = '2'× highest frequency. This is the Nyquist sampling theorem. Important for digital signal processing."
Real-World Application
An analog signal to be accurately reproduced: It must be sampled at least twice the rate of the highest frequency component of the signal. This is the Nyquist sampling theorem - sample at 2× the highest frequency. This is the frequency - at least twice the highest frequency.
Key Concepts
Why Other Options Are Wrong
Option A: Incorrect. At least half the rate isn't correct - sampling must be at least twice the highest frequency (Nyquist). Half the rate isn't correct.
Option C: Incorrect. At the same rate as highest frequency isn't correct - sampling must be at least twice the highest frequency. Same rate isn't correct.
Option D: Incorrect. At four times the rate isn't required - sampling must be at least twice the highest frequency. Four times isn't required.
题目解析
The correct answer is B: At least twice the rate of the highest frequency component of the signal. How frequently must an analog signal be sampled to be accurately reproduced is at least twice the rate of the highest frequency component of the signal. This is the Nyquist sampling theorem. For amateur radio operators, this is important for digital signal processing. Understanding this helps when working with ADCs.
考试技巧
Sampling frequency for accurate reproduction = at least twice the highest frequency component. Think 'N'yquist = 'N'eed '2'× highest frequency. This is the Nyquist sampling theorem. Not half, not same rate, not four times - just at least twice.
记忆口诀
Sampling frequency for accurate reproduction = at least twice the highest frequency component. Think 'N'yquist = '2'× highest frequency. This is the Nyquist sampling theorem. Important for digital signal processing.
实际应用示例
An analog signal to be accurately reproduced: It must be sampled at least twice the rate of the highest frequency component of the signal. This is the Nyquist sampling theorem - sample at 2× the highest frequency. This is the frequency - at least twice the highest frequency.
错误选项分析
Option A: Incorrect. At least half the rate isn't correct - sampling must be at least twice the highest frequency (Nyquist). Half the rate isn't correct. Option C: Incorrect. At the same rate as highest frequency isn't correct - sampling must be at least twice the highest frequency. Same rate isn't correct. Option D: Incorrect. At four times the rate isn't required - sampling must be at least twice the highest frequency. Four times isn't required.
知识点
How frequently, Analog signal sampled, Accurately reproduced, At least twice, Highest frequency component
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.