# Nyquist theorem vs sampling theorem vs shannon sampling theorem?

Is there any difference between these three?or these are just three names of same theorem?

• Have you already Googled the definition of each and compared? What is confusing you in that? This may be helpful in the best questions for this site: dsp.stackexchange.com/help/how-to-ask Mar 18 '20 at 17:50
• You're forgetting poor Whittaker in the list! And Kotelnikov! To quote wikipedia: "The name Nyquist–Shannon sampling theorem honours Harry Nyquist and Claude Shannon although it had already been discovered in 1933 by Vladimir Kotelnikov. The theorem was also discovered independently by E. T. Whittaker and by others. It is thus also known by the names Nyquist–Shannon–Kotelnikov, Whittaker–Shannon–Kotelnikov, and Whittaker–Nyquist–Kotelnikov–Shannon, and may also be referred to as the cardinal theorem of interpolation. " Mar 18 '20 at 18:26

Sampling operation has its roots in the mathematical interpolation theory which was used to generate certain function values at specified points from the availabe set (the samples) of existing values. These kind of work is summarized as Whittaker interpolation. Lagrange interpolation is also another related concept.

Sampling theorem in electrical engineering, however, has its roots in the communication engineering literature and pioneered by communications engineer Harry Nyquist, who was among the first to consider digital transmission of analog signals. The Nyquist sampling theorem states the minimum number of uniformly taken samples to exactly represent a given bandlimited continuous-time signal so that it (the signal) can be transmitted using digital means and reconstructed (exactly) at the receiving end.

Later, C.E.Shannon also worked on communications theory (especially the digital one) more from a probabilitistic point of view and published his conclusions as Information Theory within his classic paper of The Mathematical Theory of Communications. Among the works shannon did also include a more in depth analysis of sampling operation and resulting Shannon Sampling theorem which is identical to Nyquist sampling theorem for bandlimited signals.

Hence the uniform sampling of bandlimited continuous-time signals is referred to as Nyquist-Shannon sampling theorem. You may omit the inventors' names and simply call it sampling theorem remembering that it's the uniform sampling of bandlimited signals.

• i think Nyquist discovered the rate that sampling had to take, but did not have an explicit reconstruction scheme until Shannon and then Wittaker.. Mar 18 '20 at 22:32
• So in nutshell all these theorems are stating more or less the same idea?
– Man
Mar 19 '20 at 6:10
• @Man yes that's right, it won't harm. Mar 19 '20 at 17:33
• @robertbristow-johnson don't have an idea about that. Mar 19 '20 at 17:33