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Current fftw source
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 18 Oct 2016 13:40:26 +0100
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cannam@127 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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cannam@127 3 <!-- This manual is for FFTW
cannam@127 4 (version 3.3.5, 30 July 2016).
cannam@127 5
cannam@127 6 Copyright (C) 2003 Matteo Frigo.
cannam@127 7
cannam@127 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@127 10 Permission is granted to make and distribute verbatim copies of this
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cannam@127 24 <head>
cannam@127 25 <title>FFTW 3.3.5: Complex DFTs</title>
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cannam@127 70
cannam@127 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
cannam@127 72 <a name="Complex-DFTs"></a>
cannam@127 73 <div class="header">
cannam@127 74 <p>
cannam@127 75 Next: <a href="Planner-Flags.html#Planner-Flags" accesskey="n" rel="next">Planner Flags</a>, Previous: <a href="Basic-Interface.html#Basic-Interface" accesskey="p" rel="prev">Basic Interface</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
cannam@127 76 </div>
cannam@127 77 <hr>
cannam@127 78 <a name="Complex-DFTs-1"></a>
cannam@127 79 <h4 class="subsection">4.3.1 Complex DFTs</h4>
cannam@127 80
cannam@127 81 <div class="example">
cannam@127 82 <pre class="example">fftw_plan fftw_plan_dft_1d(int n0,
cannam@127 83 fftw_complex *in, fftw_complex *out,
cannam@127 84 int sign, unsigned flags);
cannam@127 85 fftw_plan fftw_plan_dft_2d(int n0, int n1,
cannam@127 86 fftw_complex *in, fftw_complex *out,
cannam@127 87 int sign, unsigned flags);
cannam@127 88 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
cannam@127 89 fftw_complex *in, fftw_complex *out,
cannam@127 90 int sign, unsigned flags);
cannam@127 91 fftw_plan fftw_plan_dft(int rank, const int *n,
cannam@127 92 fftw_complex *in, fftw_complex *out,
cannam@127 93 int sign, unsigned flags);
cannam@127 94 </pre></div>
cannam@127 95 <a name="index-fftw_005fplan_005fdft_005f1d-1"></a>
cannam@127 96 <a name="index-fftw_005fplan_005fdft_005f2d-1"></a>
cannam@127 97 <a name="index-fftw_005fplan_005fdft_005f3d-1"></a>
cannam@127 98 <a name="index-fftw_005fplan_005fdft-1"></a>
cannam@127 99
cannam@127 100 <p>Plan a complex input/output discrete Fourier transform (DFT) in zero or
cannam@127 101 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
cannam@127 102 </p>
cannam@127 103 <p>Once you have created a plan for a certain transform type and
cannam@127 104 parameters, then creating another plan of the same type and parameters,
cannam@127 105 but for different arrays, is fast and shares constant data with the
cannam@127 106 first plan (if it still exists).
cannam@127 107 </p>
cannam@127 108 <p>The planner returns <code>NULL</code> if the plan cannot be created. In the
cannam@127 109 standard FFTW distribution, the basic interface is guaranteed to return
cannam@127 110 a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
cannam@127 111 using a customized FFTW configuration supporting a restricted set of
cannam@127 112 transforms.
cannam@127 113 </p>
cannam@127 114 <a name="Arguments"></a>
cannam@127 115 <h4 class="subsubheading">Arguments</h4>
cannam@127 116 <ul>
cannam@127 117 <li> <code>rank</code> is the rank of the transform (it should be the size of the
cannam@127 118 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@127 119 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
cannam@127 120 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
cannam@127 121 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
cannam@127 122 copy of one number from input to output.
cannam@127 123
cannam@127 124 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
cannam@127 125 for each routine) specify the size of the transform dimensions. They
cannam@127 126 can be any positive integer.
cannam@127 127
cannam@127 128 <ul class="no-bullet">
cannam@127 129 <li>- <a name="index-row_002dmajor-1"></a>
cannam@127 130 Multi-dimensional arrays are stored in row-major order with dimensions:
cannam@127 131 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
cannam@127 132 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
cannam@127 133 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
cannam@127 134 </li><li>- FFTW is best at handling sizes of the form
cannam@127 135 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
cannam@127 136 11<sup>e</sup> 13<sup>f</sup>,where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
cannam@127 137 are arbitrary. Other sizes are computed by means of a slow,
cannam@127 138 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@127 139 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
cannam@127 140 Transforms whose sizes are powers of <em>2</em> are especially fast.
cannam@127 141 </li></ul>
cannam@127 142
cannam@127 143 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
cannam@127 144 transform, which may be the same (yielding an in-place transform).
cannam@127 145 <a name="index-in_002dplace-2"></a>
cannam@127 146 These arrays are overwritten during planning, unless
cannam@127 147 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
cannam@127 148 initialized, but they must be allocated.)
cannam@127 149
cannam@127 150 <p>If <code>in == out</code>, the transform is <em>in-place</em> and the input
cannam@127 151 array is overwritten. If <code>in != out</code>, the two arrays must
cannam@127 152 not overlap (but FFTW does not check for this condition).
cannam@127 153 </p>
cannam@127 154 </li><li> <a name="index-FFTW_005fFORWARD-2"></a>
cannam@127 155 <a name="index-FFTW_005fBACKWARD-2"></a>
cannam@127 156 <code>sign</code> is the sign of the exponent in the formula that defines the
cannam@127 157 Fourier transform. It can be <em>-1</em> (= <code>FFTW_FORWARD</code>) or
cannam@127 158 <em>+1</em> (= <code>FFTW_BACKWARD</code>).
cannam@127 159
cannam@127 160 </li><li> <a name="index-flags-2"></a>
cannam@127 161 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
cannam@127 162 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
cannam@127 163
cannam@127 164 </li></ul>
cannam@127 165
cannam@127 166 <p>FFTW computes an unnormalized transform: computing a forward followed by
cannam@127 167 a backward transform (or vice versa) will result in the original data
cannam@127 168 multiplied by the size of the transform (the product of the dimensions).
cannam@127 169 <a name="index-normalization-5"></a>
cannam@127 170 For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
cannam@127 171 </p>
cannam@127 172 <hr>
cannam@127 173 <div class="header">
cannam@127 174 <p>
cannam@127 175 Next: <a href="Planner-Flags.html#Planner-Flags" accesskey="n" rel="next">Planner Flags</a>, Previous: <a href="Basic-Interface.html#Basic-Interface" accesskey="p" rel="prev">Basic Interface</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
cannam@127 176 </div>
cannam@127 177
cannam@127 178
cannam@127 179
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cannam@127 181 </html>