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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
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<html>
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<head><title>
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FFTW FAQ - Section 3
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</title>
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<link rev="made" href="mailto:fftw@theory.lcs.mit.edu">
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<link rel="Contents" href="index.html">
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<link rel="Start" href="index.html">
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<link rel="Next" href="section4.html"><link rel="Previous" href="section2.html"><link rel="Bookmark" title="FFTW FAQ" href="index.html">
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</head><body text="#000000" bgcolor="#FFFFFF"><h1>
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FFTW FAQ - Section 3 <br>
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Using FFTW
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</h1>
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<ul>
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<li><a href="#slow" rel=subdocument>Q3.1. FFTW seems really slow.</a>
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<li><a href="#conventions" rel=subdocument>Q3.2. FFTW gives results different from my old
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FFT.</a>
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<li><a href="#savePlans" rel=subdocument>Q3.3. Can I save FFTW's plans?</a>
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<li><a href="#whyscaled" rel=subdocument>Q3.4. Why does your inverse transform return a scaled
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result?</a>
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<li><a href="#centerorigin" rel=subdocument>Q3.5. How can I make FFTW put the origin (zero frequency) at the center of
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its output?</a>
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<li><a href="#imageaudio" rel=subdocument>Q3.6. How do I FFT an image/audio file in <i>foobar</i> format?</a>
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<li><a href="#linkfails" rel=subdocument>Q3.7. My program does not link (on Unix).</a>
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</ul><hr>
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<h2><A name="slow">
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Question 3.1.  FFTW seems really slow.
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</A></h2>
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You are probably recreating the plan before every transform, rather
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than creating it once and reusing it for all transforms of the same
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size.  FFTW is designed to be used in the following way:
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<ul>
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<li>First, you create a plan.  This will take several seconds.
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<li>Then, you reuse the plan many times to perform FFTs.  These are fast.
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</ul>
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If you don't need to compute many transforms and the time for the
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planner is significant, you have two options.  First, you can use the
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<code>FFTW_ESTIMATE</code> option in the planner, which uses heuristics
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instead of runtime measurements and produces a good plan in a short
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time.  Second, you can use the wisdom feature to precompute the plan;
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see <A href="#savePlans">Q3.3 `Can I save FFTW's plans?'</A>
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<h2><A name="conventions">
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Question 3.2.  FFTW gives results different from my old
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FFT.
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</A></h2>
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People follow many different conventions for the DFT, and you should
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be sure to know the ones that we use (described in the FFTW manual).
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In particular, you should be aware that the
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<code>FFTW_FORWARD</code>/<code>FFTW_BACKWARD</code> directions correspond to signs of -1/+1 in the exponent of the DFT definition.
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(<i>Numerical Recipes</i> uses the opposite convention.)  
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<p>
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You should also know that we compute an unnormalized transform.  In
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contrast, Matlab is an example of program that computes a normalized
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transform.  See <A href="#whyscaled">Q3.4 `Why does your inverse transform return a scaled
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result?'</A>.  
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<h2><A name="savePlans">
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Question 3.3.  Can I save FFTW's plans?
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</A></h2>
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Yes. Starting with version 1.2, FFTW provides the
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<code>wisdom</code> mechanism for saving plans.  See <A href="section4.html#wisdom">Q4.3 `What is this <code>wisdom</code> thing?'</A> and the FFTW manual.  
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<h2><A name="whyscaled">
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Question 3.4.  Why does your inverse transform return a scaled
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result?
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</A></h2>
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Computing the forward transform followed by the backward transform (or
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vice versa) yields the original array scaled by the size of the array.
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 (For multi-dimensional transforms, the size of the array is the
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product of the dimensions.)  We could, instead, have chosen a
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normalization that would have returned the unscaled array. Or, to
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accomodate the many conventions in this matter, the transform routines
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could have accepted a &quot;scale factor&quot; parameter. We did not
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do this, however, for two reasons. First, we didn't want to sacrifice
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performance in the common case where the scale factor is 1. Second, in
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real applications the FFT is followed or preceded by some computation
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on the data, into which the scale factor can typically be absorbed at
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little or no cost.  
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<h2><A name="centerorigin">
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Question 3.5.  How can I make FFTW put the origin (zero frequency) at
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the center of its output?
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</A></h2>
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For human viewing of a spectrum, it is often convenient to put the
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origin in frequency space at the center of the output array, rather
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than in the zero-th element (the default in FFTW).  If all of the
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dimensions of your array are even, you can accomplish this by simply
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multiplying each element of the input array by (-1)^(i + j + ...),
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where i, j, etcetera are the indices of the element.  (This trick is a
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general property of the DFT, and is not specific to FFTW.)
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<h2><A name="imageaudio">
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Question 3.6.  How do I FFT an image/audio file in
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<i>foobar</i> format?
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</A></h2>
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FFTW performs an FFT on an array of floating-point values.  You can
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certainly use it to compute the transform of an image or audio stream,
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but you are responsible for figuring out your data format and
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converting it to the form FFTW requires.
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<h2><A name="linkfails">
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Question 3.7.  My program does not link (on
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Unix).
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</A></h2>
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Please use the exact order in which libraries are specified by the
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FFTW manual (e.g. <code>-lrfftw -lfftw -lm</code>).  Also, note that the libraries must be listed after your program sources/objects.  (The
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general rule is that if <i>A</i> uses <i>B</i>, then <i>A</i> must be listed before <i>B</i> in the link command.).  For example, switching the order to <code>-lfftw -lrfftw -lm</code> will fail.  <hr>
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Next: <a href="section4.html" rel=precedes>Internals of FFTW</a>.<br>
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Back: <a href="section2.html" rev=precedes>Installing FFTW</a>.<br>
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<a href="index.html" rev=subdocument>Return to contents</a>.<p>
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<address>
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<A href="http://theory.lcs.mit.edu/~fftw/">Matteo Frigo and Steven G. Johnson</A> / <A href="mailto:fftw@theory.lcs.mit.edu">fftw@theory.lcs.mit.edu</A>
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- 18 May 1999
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</address><br>
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Extracted from FFTW Frequently Asked Questions with Answers,
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Copyright &copy; 1999 Massachusetts Institute of Technology.
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