Discrete Fourier Transforms

Discrete Fourier Transform (DFT) transforms any signal from its time/space domain into a related signal in frequency domain. This allows us not only to analyze the different frequencies of the data, but also enables faster filtering operations, when used properly. It is possible to turn a signal in frequency domain back to its time/spatial domain, thanks to the Inverse Fourier Transform (IFT). We will not go into details of the mathematics behind these operators, since we assume familiarity at some level with this theory. We will focus on syntax and applications instead.

The basic routines in the scipy.fftpack module compute the DFT and its inverse, for discrete signals in any dimension – fft, ifft (one dimension); fft2, ifft2 (two dimensions); fftn, ifftn (any number of dimensions). All of these routines assume that the data is complex valued. If we know beforehand that a particular dataset is actually real valued, and should offer real-valued frequencies...