Final answer:
Sampling at a rate less than twice the highest frequency in a signal leads to aliasing, as stated by the Nyquist-Shannon sampling theorem. Aliasing causes higher-frequency signals to be misrepresented as lower-frequency signals, which can result in signal distortion and loss of information.
Step-by-step explanation:
If the rate of sampling is less than twice the highest frequency in the signal, also known as under-sampling, it leads to a phenomenon called aliasing. Aliasing occurs when higher-frequency signals are misrepresented as lower-frequency signals. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency of the signal (the Nyquist rate). If not, the signal can't be uniquely reconstructed from its samples.
Aliasing makes different signals indistinguishable (or aliases of one another) when sampled, leading to distortion and loss of information. This is crucial in fields like digital signal processing, communications, and data conversion where maintaining signal integrity is essential.
For example, if an audio signal that contains a 22 kHz frequency component were sampled at 30 kHz, which is less than twice the 22 kHz frequency, the result would be an incorrect representation of the original signal when played back. Instead of the 22 kHz tone, a 8 kHz tone (30 kHz - 22 kHz) would be heard due to aliasing. This simplified example highlights the importance of following the Nyquist criterion to avoid such issues.