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Add FFTW3
author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
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cannam@95 1 <html lang="en">
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cannam@95 3 <title>Complex DFTs - FFTW 3.3.3</title>
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cannam@95 13 This manual is for FFTW
cannam@95 14 (version 3.3.3, 25 November 2012).
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cannam@95 16 Copyright (C) 2003 Matteo Frigo.
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cannam@95 18 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@95 48 <div class="node">
cannam@95 49 <a name="Complex-DFTs"></a>
cannam@95 50 <p>
cannam@95 51 Next:&nbsp;<a rel="next" accesskey="n" href="Planner-Flags.html#Planner-Flags">Planner Flags</a>,
cannam@95 52 Previous:&nbsp;<a rel="previous" accesskey="p" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>,
cannam@95 53 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
cannam@95 54 <hr>
cannam@95 55 </div>
cannam@95 56
cannam@95 57 <h4 class="subsection">4.3.1 Complex DFTs</h4>
cannam@95 58
cannam@95 59 <pre class="example"> fftw_plan fftw_plan_dft_1d(int n0,
cannam@95 60 fftw_complex *in, fftw_complex *out,
cannam@95 61 int sign, unsigned flags);
cannam@95 62 fftw_plan fftw_plan_dft_2d(int n0, int n1,
cannam@95 63 fftw_complex *in, fftw_complex *out,
cannam@95 64 int sign, unsigned flags);
cannam@95 65 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
cannam@95 66 fftw_complex *in, fftw_complex *out,
cannam@95 67 int sign, unsigned flags);
cannam@95 68 fftw_plan fftw_plan_dft(int rank, const int *n,
cannam@95 69 fftw_complex *in, fftw_complex *out,
cannam@95 70 int sign, unsigned flags);
cannam@95 71 </pre>
cannam@95 72 <p><a name="index-fftw_005fplan_005fdft_005f1d-161"></a><a name="index-fftw_005fplan_005fdft_005f2d-162"></a><a name="index-fftw_005fplan_005fdft_005f3d-163"></a><a name="index-fftw_005fplan_005fdft-164"></a>
cannam@95 73 Plan a complex input/output discrete Fourier transform (DFT) in zero or
cannam@95 74 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
cannam@95 75
cannam@95 76 <p>Once you have created a plan for a certain transform type and
cannam@95 77 parameters, then creating another plan of the same type and parameters,
cannam@95 78 but for different arrays, is fast and shares constant data with the
cannam@95 79 first plan (if it still exists).
cannam@95 80
cannam@95 81 <p>The planner returns <code>NULL</code> if the plan cannot be created. In the
cannam@95 82 standard FFTW distribution, the basic interface is guaranteed to return
cannam@95 83 a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
cannam@95 84 using a customized FFTW configuration supporting a restricted set of
cannam@95 85 transforms.
cannam@95 86
cannam@95 87 <h5 class="subsubheading">Arguments</h5>
cannam@95 88
cannam@95 89 <ul>
cannam@95 90 <li><code>rank</code> is the rank of the transform (it should be the size of the
cannam@95 91 array <code>*n</code>), and can be any non-negative integer. (See <a href="Complex-Multi_002dDimensional-DFTs.html#Complex-Multi_002dDimensional-DFTs">Complex Multi-Dimensional DFTs</a>, for the definition of &ldquo;rank&rdquo;.) The
cannam@95 92 &lsquo;<samp><span class="samp">_1d</span></samp>&rsquo;, &lsquo;<samp><span class="samp">_2d</span></samp>&rsquo;, and &lsquo;<samp><span class="samp">_3d</span></samp>&rsquo; planners correspond to a
cannam@95 93 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
cannam@95 94 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
cannam@95 95 copy of one number from input to output.
cannam@95 96
cannam@95 97 <li><code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
cannam@95 98 for each routine) specify the size of the transform dimensions. They
cannam@95 99 can be any positive integer.
cannam@95 100
cannam@95 101 <ul>
cannam@95 102 <li><a name="index-row_002dmajor-165"></a>Multi-dimensional arrays are stored in row-major order with dimensions:
cannam@95 103 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
cannam@95 104 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
cannam@95 105 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
cannam@95 106 <li>FFTW is best at handling sizes of the form
cannam@95 107 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
cannam@95 108 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
cannam@95 109 are arbitrary. Other sizes are computed by means of a slow,
cannam@95 110 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>) performance even for prime sizes). It is possible to customize FFTW
cannam@95 111 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
cannam@95 112 Transforms whose sizes are powers of 2 are especially fast.
cannam@95 113 </ul>
cannam@95 114
cannam@95 115 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
cannam@95 116 transform, which may be the same (yielding an in-place transform).
cannam@95 117 <a name="index-in_002dplace-166"></a>These arrays are overwritten during planning, unless
cannam@95 118 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
cannam@95 119 initialized, but they must be allocated.)
cannam@95 120
cannam@95 121 <p>If <code>in == out</code>, the transform is <dfn>in-place</dfn> and the input
cannam@95 122 array is overwritten. If <code>in != out</code>, the two arrays must
cannam@95 123 not overlap (but FFTW does not check for this condition).
cannam@95 124
cannam@95 125 <li><a name="index-FFTW_005fFORWARD-167"></a><a name="index-FFTW_005fBACKWARD-168"></a><code>sign</code> is the sign of the exponent in the formula that defines the
cannam@95 126 Fourier transform. It can be -1 (= <code>FFTW_FORWARD</code>) or
cannam@95 127 +1 (= <code>FFTW_BACKWARD</code>).
cannam@95 128
cannam@95 129 <li><a name="index-flags-169"></a><code>flags</code> is a bitwise OR (&lsquo;<samp><span class="samp">|</span></samp>&rsquo;) of zero or more planner flags,
cannam@95 130 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
cannam@95 131
cannam@95 132 </ul>
cannam@95 133
cannam@95 134 <p>FFTW computes an unnormalized transform: computing a forward followed by
cannam@95 135 a backward transform (or vice versa) will result in the original data
cannam@95 136 multiplied by the size of the transform (the product of the dimensions).
cannam@95 137 <a name="index-normalization-170"></a>For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
cannam@95 138
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