I am seeking explanation of what "Fourier method" is that is described for resampling in documentation of resample() method. I want to downsample an array. I know what decimation is and how it works, I also know what fourier transform is. I cannot however find "scientific backup" so to say to the resample method in scipy. I saw this topic:
Python's $\tt resample$ vs $\tt resample\_poly$ vs $\tt decimate$
I also searched across some books regarding digital signal processing. Am I missing something obvious? I looked in the implementation of resample and I know it performs fourier transform on signal and then takes half of samples needed from the beginning of transformed array and from the end. Then it inverses fourier transform coming back to time-domain. I cannot find scientific description of this method. In the link above, this was mentioned:
I don't understand how interpolation is connected with downsampling. Could anyone explain and/or link some resources? Scipy docs has this in method description:
num samples using Fourier method along the given axis.
The resampled signal starts at the same value as `x` but is sampled with a spacing of ``len(x) / num * (spacing of x)``. Because a Fourier method is used, the signal is assumed to be periodic.
Thanks in advance.