According to the Nyquist criterion, what is the minimum sampling rate required to accurately sample a signal with a maximum frequency component of 3 kHz?

According to the Nyquist criterion, what is the minimum sampling rate required to accurately sample a signal with a maximum frequency component of 3 kHz?

• A. At least 6 kHz
• B. At least 3 kHz
• C. At least 12 kHz
• D. At least 1.5 kHz

Answer: (A)

Nyquist sampling theorem requires sampling at least twice the highest frequency present in a signal to capture all its information and avoid aliasing. For a signal with a maximum frequency of 3 kHz, the smallest rate that meets this condition is 2 × 3 kHz = 6 kHz. Sampling at 6 kHz avoids aliasing and is the minimum needed. Sampling lower (for example, 3 kHz or 1.5 kHz) would cause the 3 kHz component to fold into lower frequencies, corrupting the signal. Sampling higher (like 12 kHz) also works, but it’s not the minimum.

Nyquist sampling theorem requires sampling at least twice the highest frequency present in a signal to capture all its information and avoid aliasing. For a signal with a maximum frequency of 3 kHz, the smallest rate that meets this condition is 2 × 3 kHz = 6 kHz. Sampling at 6 kHz avoids aliasing and is the minimum needed. Sampling lower (for example, 3 kHz or 1.5 kHz) would cause the 3 kHz component to fold into lower frequencies, corrupting the signal. Sampling higher (like 12 kHz) also works, but it’s not the minimum.