Everything about Nyquist Rate totally explained
In
signal processing, the
Nyquist rate is two times the
bandwidth—but this concept has two rather different meanings: as a lower bound for the sample rate for alias-free signal sampling, and as an upper bound for the signaling rate across a bandwidth-limited channel such as a telegraph line.
Sampling at the Nyquist rate
The Nyquist rate is the minimum
sampling rate required to avoid
aliasing, equal to twice the highest
modulation frequency contained within the signal. In other words, the Nyquist rate is equal to the two-sided
bandwidth of the signal (the
upper and
lower sidebands).
»
where
is the highest
frequency at which the signal can have nonzero energy.
To avoid aliasing, the sampling rate must exceed the Nyquist rate:
»
Signaling at the Nyquist rate
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 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 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 as in the original)
According to the
OED, this may be the origin of the term
Nyquist rate.
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.
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 didn't 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."
Further Information
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