Editing Nyquist rate (section)

==Relative to signaling==

Long before [[Harry Nyquist]] had his name associated with sampling, the term ''Nyquist rate'' was used differently, with a meaning closer to what Nyquist actually studied.  Quoting [[Harold Stephen Black|Harold S. Black's]] 1953 book ''Modulation Theory,'' in the section '''''Nyquist Interval''''' of the opening chapter ''Historical Background:''

:"If the essential frequency range is limited to ''B'' cycles per second, 2''B'' was given by Nyquist as the maximum number of code elements per second that could be unambiguously resolved, assuming the peak interference is less than half a quantum step.  This rate is generally referred to as '''signaling at the Nyquist rate''' and 1/(2''B'') has been termed a ''Nyquist interval''." (bold added for emphasis; italics from the original)

''B'' in this context, related to the [[Nyquist ISI criterion]], referring to the one-sided bandwidth rather than the total as considered in later usage.

According to the [[Oxford English Dictionary|OED]], Black's statement regarding 2''B'' may be the origin of the term ''Nyquist rate''.<ref name=Black/>

Nyquist's famous 1928 paper was a study on how many pulses (code elements) could be transmitted per second, and recovered, through a channel of limited bandwidth.<ref name=Nyquist/>
''Signaling at the Nyquist rate'' meant putting as many code pulses through a telegraph channel as its bandwidth would allow.  Shannon used Nyquist's approach when he proved the [[sampling theorem]] in 1948, but Nyquist did not work on sampling per se.

Black's later chapter on "The Sampling Principle" does give Nyquist some of the credit for some relevant math:

:"Nyquist (1928) pointed out that, if the function is substantially limited to the time interval ''T'', 2''BT'' values are sufficient to specify the function, basing his conclusions on a Fourier series representation of the function over the time interval ''T''."