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 fftw3 (in OSX with MacPorts: sudo port install fftw3) sudo gem install fftw3
How to use
See the following peice of code. (Install this library and copy and paste the following to the interactive shell irb).
require "fftw3" na = NArray.float(8,6) # float -> will be corced to complex na[1,1]=1 # <example 1> fc = FFTW3.fft(na)/na.length # forward 2D FFT and normalization nc = FFTW3.ifft(fc) # backward 2D FFT (complex) --> nb = nc.real # should be equal to na except round errors # <example 2> fc = FFTW3.fft(na, 0) / na.shape # forward FFT with the first dim # <example 3> fc = FFTW3.fft(na, 1) / na.shape # forward FFT with the second 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. * 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.
Complex inverse FFT