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16.3 fftpack Python Interface

16.3 fftpack Python Interface

The interface to the FFTPACK library is performed via the fftpack module, which is responsible for making sure that the arrays sent to the FFTPACK routines are in the right format (contiguous memory locations, right numerical storage format, etc). It provides interfaces to the following FFTPACK routines, which are also the names of the Python functions:

cffti( i)
cfftf( data, savearea)
cfftb( data, savearea)
rffti( i)
rfftf( data, savearea)
rfftb( data, savearea)
The routines which start with c expect arrays of complex numbers, the routines which start with r expect real numbers only. The routines which end with i are the initalization functions, those which end with f perform the forward FFTs and those which end with b perform the backwards FFTs.

The initialization functions require a single integer argument corresponding to the size of the dataset, and returns a work array. The forward and backwards FFTs require two array arguments - the first is the data array, the second is the work array returned by the initialization function. They return arrays corresponding to the coefficients of the FFT, with the first element in the returned array corresponding to the DC component, the second one to the first fundamental, etc.The length of the returned array is 1 + half the length of the input array in the case of real FFTs, and the same size as the input array in the case of complex data.

>>> import numarray.fft.fftpack as fftpack
>>> x = cos(arange(30.0)/30.0*2*pi)
>>> w = fftpack.rffti(30)
>>> f = fftpack.rfftf(x, w)
>>> print f[0:5]
[ -5.68989300e-16 +0.00000000e+00j   1.50000000e+01 -3.08862614e-15j
        6.86516117e-16 -1.00588467e-15j   1.12688689e-15 -3.19983494e-15j
       -1.52158521e-15 +1.14787259e-15j]

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