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So I've been searched online and can't seem to find a clear cut answer to this question.

From my understanding, the Nyquist rate is double of the maximum frequency of a signal which Nyquist frequency is half of the Nyquist rate.

Which would conclude that Nyquist rate is the lower bound of sampling and Nyquist frequency would be the upper bound where Nyquist rate is where you can preserve the original signal and anything in between the Nyquist rate to Nyquist frequency would cause some aliasing.

Is this correct?

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  • $\begingroup$ Welcome to DSP.SE! The Wikipedia pages for both terms support your assessment. It depends on whether you want to stop aliasing by choosing the sampling rate based on your signal or stop aliasing by limiting your signal based on your available sampling rate. $\endgroup$
    – Peter K. ♦
    Oct 29, 2015 at 9:01
  • $\begingroup$ The answers are right, but they leave out the fact that having too much bandwidth for the sampling rate will result in spurious frequencies appearing in the analysis; bogus signals. $\endgroup$
    – rrogers
    Oct 5, 2021 at 20:41

2 Answers 2

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Harry Nyquist invented/discovered/proved a lot of things; it can be hard to keep track of them all. The three most important for signal processing and communications are probably these:

  • If you sample a (real) signal $s(t)$ at $f_s>2B$ samples per second, then $s(t)$ can be reconstructed from its samples, where $B$ is the bandwidth of $s(t)$. The lower bound $2B$ is often called the Nyquist rate.

  • If you sample a signal $s(t)$ at $f_s$ samples per second, then $f_N=f_s/2$ is frequently called the Nyquist frequency (also folding frequency). All frequencies in $s(t)$ higher than $f_N$ will be aliased back to a frequency between 0 and $f_N$.

  • Assume you have a baseband channel of bandwidth $B$ (that is, signals with bandwidth $B$ or less are not distorted by the channel). This channel allows transmission of a maximum of $2B$ orthogonal pulses per second. $2B$ in this context is also called the Nyquist rate.

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These terms are indeed named in a confusing manner, as frequency and rate are pretty much synonyms. Either way:

Nyquist frequency is the maximum frequency in a signal
that can be well recorded given a certain
sampling rate.

Nyquist rate is the sampling rate
needed to record signal well given a certain
maximum frequency in a signal.

given sampling rate = nyquist frequency * 2
nyquist rate = given max frequency * 2

So if we have a fixed sampling rate and want to decide which frequencies to cut off in a signal so that we don't get aliasing - we want to know Nyquist frequency.

But if we have a fixed maximum frequency in a signal, and we are ready to accommodate our sampling rate - we want to know Nyquist rate.

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