Question

Aliasing occurs when,

• A. Sampling rate is higher than Nyquist rate
• B. Sampling rate is lower than Nyquist rate
• C. Signal is periodic
• D. Signal is even

Hint:

To prevent aliasing in practical systems:
1. Pass the analog signal through an anti-aliasing low-pass filter to remove any frequency components above $f_s/2$ before sampling.
2. Ensure the sampling rate of the analog-to-digital converter (ADC) is chosen such that $f_s \geq 2 f_{max}$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question asks for the fundamental condition under which the frequency-domain distortion known as aliasing occurs during the signal sampling process.

Step 2: Key Formula or Approach:
Let $f_s$ be the sampling rate and $f_N = 2 f_{max}$ be the Nyquist rate, where $f_{max}$ is the highest frequency component present in the band-limited signal.
The condition for aliasing to occur is:
\[ f_s < f_N \]

Step 3: Detailed Explanation:

• Sampling a continuous-time signal in the time domain corresponds to the periodic replication of its spectrum in the frequency domain at integer multiples of the sampling frequency ($f_s$).

• If the sampling frequency is equal to or greater than twice the maximum frequency component of the signal ($f_s \geq 2 f_{max}$), the spectral replicas are sufficiently separated.

• In this case, an ideal low-pass filter with a suitable cutoff frequency can isolate the original spectrum, allowing for perfect reconstruction without any loss of information.

• If the sampling rate is lower than the Nyquist rate ($f_s < 2 f_{max}$), the adjacent spectral replicas overlap with each other.

• This overlapping makes it impossible to separate the original spectrum from its replicas.

• During reconstruction, high-frequency components are folded back into the lower frequency range, appearing as lower-frequency signals (aliases).

• This phenomenon is called aliasing, and it represents an irreversible loss of the original signal's high-frequency details.

Step 4: Final Answer
Thus, aliasing occurs when the sampling rate is lower than the Nyquist rate, which corresponds to option (B).