Sampling Theorem and Aliasing The sampling theorem states that a continuous-time signal can be perfectly reconstructed from its discrete-time samples if...
The sampling theorem states that a continuous-time signal can be perfectly reconstructed from its discrete-time samples if the sampling rate is greater than twice the highest frequency component in the signal.
This means that:
Sampling rate > 2f_max: The continuous-time signal can be perfectly reconstructed from the discrete-time samples.
Sampling rate <= 2f_max: The continuous-time signal cannot be perfectly reconstructed from the discrete-time samples, but it can be approximated to within a certain error.
Where:
The aliasing effect occurs when a continuous-time signal is sampled at a frequency less than twice the highest frequency component. This causes a distortion in the reconstructed discrete-time signal, making it impossible to perfectly reconstruct the original continuous-time signal.
Example:
Imagine a continuous-time signal with a maximum frequency of 10 kHz. If the sampling rate is less than 20 kHz, the sampling theorem guarantees perfect reconstruction of the original signal from the discrete-time samples.
However, if the sampling rate is 15 kHz, the aliasing effect will become noticeable, causing the reconstructed discrete-time signal to deviate from the original continuous-time signal.
The sampling theorem and aliasing are important concepts in mixed-signal IC design, as they determine the achievable sampling rate and the quality of the reconstruction achievable from a continuous-time signal sampled at a specific frequency