Fast Fourier Transforms by using ((<FFTW|URL:www.fftw.org>)) Ver.3.
(C) Takeshi Horinouchi / GFD Dennou Club, 2003
Multi-dimensional complex FFT. (Real data are coerced to complex).
Supports both double and single float transforms.
Not normalized as in FFTW
Features yet to be introduced
Sine / cosine transforms
User choice of optimization levels (i.e., FFTW_MEASURE etc in addition to FFTW_ESTIMATE).
Multi-threaded FFT3 support – don't know whether it's really feasible.
Install ((<FFTW|URL:www.fftw.org>)) Ver.3.
NOTE: To activate the single-float transform, you have to install FFTW3 with the single-float compilation, in addition to the default double-float version. This can be done by configuring FFTW3 with the –enable-float option, and install it again. The single-float version will coexist with the double-float version. If you do not install the single-float version, FFT is always done with the double precision, which is not bad if you are not time- and memory-conscious.
Then, install this library as follows (replace “version” with the actual version number):
% tar xvzf fftw3-version.tar.gz % cd fftw3-version % ruby extconf.rb % make % make site-install
% make install
(If you are using Ruby 1.8, make install is the same make site-install.)
How to use
See the following peice of code. (Install this library and copy and paste the following to the interactive shell irb).
require "narray" require "numru/fftw3" include NumRu na = NArray.float(8,6) # float -> will be corced to complex na[1,1]=1 # <example 1> fc = FFTW3.fft(na, -1)/na.length # forward 2D FFT and normalization nc = FFTW3.fft(fc, 1) # backward 2D FFT (complex) --> nb = nc.real # should be equal to na except round errors # <example 2> fc = FFTW3.fft(na, -1, 0) / na.shape # forward FFT with the first dim # <example 3> fc = FFTW3.fft(na, -1, 1) / na.shape # forward FFT with the second dim
—fft(narray, dir [,dim,dim,…])
Complex FFT. The 3rd, 4th,... arguments are optional. ARGUMENTS * narray (NArray or NArray-compatible Array) : array to be transformed. If real, coerced to complex before transformation. If narray is single-precision and the single-precision version of FFTW3 is installed (before installing this module), this method does a single-precision transform. Otherwise, a double-precision transform is used. * dir (-1 or 1) : forward transform if -1; backward transform if 1. * optional 3rd, 4th,... arguments (Integer) : Specifies dimensions to apply FFT. For example, if 0, the first dimension is transformed (1D FFT); If -1, the last dimension is used (1D FFT); If 0,2,4, the first, third, and fifth dimensions are transformed (3D FFT); If entirely omitted, ALL DIMENSIONS ARE SUBJECT TO FFT, so 3D FFT is done with a 3D array. RETURN VALUE * a complex NArray NOTE * As in FFTW, return value is NOT normalized. Thus, a consecutive forward and backward transform would multiply the size of data used for transform. You can normalize, for example, the forward transform FFTW.fft(narray, -1, 0, 1) (FFT regarding the first (dim 0) & second (dim 1) dimensions) by dividing with (narray.shape*narray.shape). Likewise, the result of FFTW.fft(narray, -1) (FFT for all dimensions) can be normalized by narray.length.