# [Numpy-discussion] "Nyquist frequency" in numpy.fft docstring

Fabrice Silva silva@lma.cnrs-mrs...
Sun Jul 11 21:09:47 CDT 2010

```Le dimanche 11 juillet 2010 à 16:13 -0700, David Goldsmith a écrit :
> Hi!  I'm a little confused: in the docstring for numpy.fft we find the
> following:
>
> "For an even number of input points, A[n/2] represents both positive
> and negative Nyquist frequency..."
>
> but according to http://en.wikipedia.org/wiki/Nyquist_frequency (I
> know, I know, I've bad mouthed Wikipedia in the past, but that's in a
> different context):
>
> "The Nyquist frequency...is half the sampling frequency of a discrete
> signal processing system...The Nyquist frequency should not be
> confused with the Nyquist rate, which is the lower bound of the
> sampling frequency that satisfies the Nyquist sampling criterion for a
> given signal or family of signals...Nyquist rate, as commonly used
> with respect to sampling, is a property of a continuous-time signal,
> not of a system, whereas Nyquist frequency is a property of a
> discrete-time system, not of a signal."
>
> Yet earlier in numpy.fft's docstring we find:
>
> "...the discretized input to the transform is customarily referred to
> as a signal..."
>
> Should we be using "Nyquist rate" instead of "Nyquist frequency," and
> if not, why not?

To go further, Nyquist frequency (and also the sampling frequency) is in
fact a property of a sampling system. When dealing with fft, we are
handling the *output of such a system* (the sampled signal). Calling
A[n/2] then Nyquist frequency is then adequate.

The Nyquist rate is something you must care about *before* the
analog-digital conversion, considering the spectral content of the
continuous time signal.

My 2 pesos,
Fabricio

```