Sampling Theorem
Sampling Theorem — Defines the sampling condition required to reconstruct a band-limited continuous signal from discrete samples.
Technical Context
Defines the sampling condition required to reconstruct a band-limited continuous signal from discrete samples.
The sampling condition is not only a digital sample-rate choice; band limitation and the analogue anti-aliasing filter belong to the same acquisition assumption.
Related Articles
Naming and Scope
Sampling theorem and Nyquist-Shannon Sampling Theorem refer to the same foundational result; the former is the generic name and the latter the established eponym. They are not independent theorems.
The reconstruction result assumes a band-limited signal, ideal sampling, and a suitable reconstruction process. Real acquisition chains additionally contain ADC quantization, clock jitter, sensor noise, and finite-order filters. Satisfying the sampling condition does not remove those error sources.
Related: Sample Rate, Sampling Rate, Aliasing, Sound from the Perspective of Basic Sciences.