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

Eric Firing efiring@hawaii....
Sun Jul 11 18:42:04 CDT 2010


On 07/11/2010 01:13 PM, David Goldsmith wrote:
> 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
> <http://en.wikipedia.org/wiki/Sampling_frequency> of a discrete signal
> <http://en.wikipedia.org/wiki/Discrete_signal> processing system...The
> Nyquist frequency should not be confused with the /Nyquist rate
> <http://en.wikipedia.org/wiki/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
> <http://en.wikipedia.org/wiki/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?

No, because we are dealing with a discrete time series, and our usage 
corresponds exactly with the Wikipedia description that you quote.

Eric

>
> DG
>
>
>
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