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This directory contains files that allow you to call FFTW from MATLAB
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(instead of MATLAB's own FFT functions). This is accomplished by
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means of a "MEX" program--a MATLAB external function--that wraps
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around the FFTW library.
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NOTE: you must have MATLAB 5.0 or later to use these routines.
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Once you have compiled and installed the MEX (see below), using FFTW
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from within MATLAB is simple:
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The forward transform:
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The backwards transform:
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Note that FFTW computes the unnormalized DFT, so "c" in the above code
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is a scaled version of the original "a". (To get back the original
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"a", you would compute: c / prod(size(c)).)
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To get help on using FFTW in MATLAB, simply type "help fftw" at the
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There are a few points that you should be aware of:
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* The first call is expensive:
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The first time you call FFTW from within MATLAB, it performs
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expensive one-time computations. (It is figuring out a "plan"--see
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the FFTW manual for more information on what is happening.) So, the
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first FFT you compute is slow (it probably takes several seconds).
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However, subsequent transforms of the same size will reuse the initial
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computations, and will be quite fast (often 2-3 times as fast as
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MATLAB's built-in FFT). So, you should use FFTW within MATLAB when
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you are computing many FFTs of the same size and the initial cost is
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unimportant. If you just need a single FFT, use MATLAB's built-in
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To reduce the startup cost, at some slight penalty in performance,
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replace FFTW_MEASURE in fftw.c with FFTW_ESTIMATE.
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* Small transforms are inefficient:
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There is a certain amount of overhead involved in calling FFTW from
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MATLAB, and this makes small transforms relatively inefficient. So,
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if you are doing very small transforms in MATLAB, you might be better
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off with the built-in routines. (The exact point at which FFTW begins
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to win will depend upon your machine. It is simple for you to use
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MATLAB's timing routines to find out what is best in your
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(One of the major costs is in translating the array from MATLAB's
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representation, in which real and imaginary parts are stored
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separately, to FFTW's representation, in which complex numbers are
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stored as adjacent real/imaginary pairs.)
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* FFTW computes multi-dimensional transforms:
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The FFTW call in MATLAB computes a transform of the same
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dimensionality as the matrix that you give it. Thus, it is analogous
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to the "fftn" routine in MATLAB, rather than the "fft" routine.
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* All transforms are out-of-place:
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Although the FFTW library is capable of performing in-place
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multi-dimensional transforms, the MATLAB routine is out-of-place.
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This is simply a restriction of the environment--as far as we can
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tell, we are not allowed to modify the inputs that are passed to us,
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and must return our results in a separate array.
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**********************************************************************
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Installation of the FFTW MEX routines is straightforward. First, you
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have to compile the FFTW library (see the FFTW manual). Then, you must
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compile the file fftw.c in this directory using the MEX compilation
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procedure on your machine. Finally, you take the MEX file that is
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produced, along with the fftw.m file in this directory, and install
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them wherever you typically put your MATLAB scripts.
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The method for compiling MEX files should be described in your MATLAB
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manual. (You will need to link with the FFTW library that you had
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compiled earlier.) On UNIX systems, you can simply type "make", and
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the Makefile in this directory should do the right thing.
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matlab/README
