11. This result, usually attributed to Shannon, is known as the Nyquist Shannon sampling theorem . 12. The sampling theorem provides only a sufficient condition for perfect reconstruction, not a necessary condition. 13. The image shows the effects of aliasing when the sampling theorem 's condition is not satisfied. 14. Multidimensional sampling is similar to classical sampling as it must adhere to the Nyquist Shannon sampling theorem . 15. However, the sampling theorem can be extended in a straightforward way to functions of arbitrarily many variables. 16. The Nyquist & ndash; Shannon sampling theorem is critical for understanding the output of such discrete transforms. 17. A sampling method fundamentally different from classical fixed-rate sampling cannot " violate " the sampling theorem . 18. The mathematical limits for noise removal are set by information theory, namely the Nyquist Shannon sampling theorem . 19. The choice of sample rate used in a digital system is based on the Nyquist-Shannon sampling theorem . 20. This is a misconception, because the sampling theorem guarantees perfect reconstruction given sufficient, not necessary, conditions.
