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