Definition of Nyquist Frequency
The Nyquist frequency is the highest frequency that can be unambiguously represented in a digitally sampled signal. It is exactly half of the sampling rate used to convert an analog signal into a digital one. This concept is fundamental to avoiding aliasing, a distortion where high-frequency components in the original signal appear as lower frequencies in the sampled data.
Importance in Digital Sampling
According to the Nyquist-Shannon sampling theorem, to perfectly reconstruct a continuous analog signal from its discrete samples, the sampling rate must be at least twice the highest frequency component present in the original signal. The Nyquist frequency represents this critical upper limit for accurately capturing signal variations without loss of information or introduction of spurious components.
A Practical Example
Imagine you are recording an audio signal, and your recording device samples the sound at a rate of 44,100 samples per second (44.1 kHz). The Nyquist frequency for this system would be 22,050 Hz (22.05 kHz). This means any sound frequencies above 22.05 kHz in the original audio, such as very high-pitched whistles, cannot be accurately captured and might instead be misinterpreted as lower, incorrect frequencies (aliasing) in the digital recording.
Applications and Implications
The Nyquist frequency is crucial in various fields, including telecommunications, digital audio and video recording, medical imaging, and scientific data acquisition. Engineers and scientists must ensure that their chosen sampling rate is sufficiently high to exceed twice the maximum frequency of interest in the signal being measured. If the signal contains frequencies above the Nyquist limit, anti-aliasing filters are typically applied before sampling to remove these problematic high-frequency components.