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fftw
Some functions in the fftw
fast Fourier transform library are
callable by virtual code programs of the form
library('fftw',f)
, where f
can be one of the following
character strings.
u_fw_dft
(uni-dimensional forward Discrete Fourier transform)
u_bw_dft
(uni-dimensional backward Discrete Fourier transform)
b_fw_dft
(bi-dimensional forward Discrete Fourier transform)
b_bw_dft
(bi-dimensional backward Discrete Fourier transform)
u_dht
(uni-dimensional Discrete Hartley transform)
b_dht
(bi-dimensional Discrete Hartley transform)
These stand for the discrete Fourier transform, in one dimension and two
dimensions, either backward or forward, and the discrete Hartley
transform in one dimension and two dimensions. The fftw
library
documentation (http://www.fftw.org) can give more information
about the meaning of these transformations.
The interface is somewhat simplified compared to the API for the fftw
C library because there are no considerations of memory management or
planning, nor any provision for dimensions higher than two.
Furthermore, from the virtual side of the interface, these
functions operate on lists rather than arrays. The one dimensional
Fourier transforms take a list of complex numbers to a list of complex
numbers (see complex
), and the one dimensional Hartley
transforms take a list of reals to a list of reals (see
math
). The two dimensional transforms are analogous but they
take a matrix represented as a list of lists. Error messages
pertaining to invalid input documented at the beginning of
this section (External Libraries) are relevant.
Finally, unlike the native API for fftw
, these transformations are
scaled so that the backward transformation is the inverse of the
forward, and the Hartley transformations are their own inverses
(subject to roundoff error).
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