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Current fftw source
author Chris Cannam
date Tue, 18 Oct 2016 13:40:26 +0100
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Chris@42 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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Chris@42 3 <!-- This manual is for FFTW
Chris@42 4 (version 3.3.5, 30 July 2016).
Chris@42 5
Chris@42 6 Copyright (C) 2003 Matteo Frigo.
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Chris@42 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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Chris@42 11 manual provided the copyright notice and this permission notice are
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Chris@42 24 <head>
Chris@42 25 <title>FFTW 3.3.5: Complex DFTs</title>
Chris@42 26
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Chris@42 70
Chris@42 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
Chris@42 72 <a name="Complex-DFTs"></a>
Chris@42 73 <div class="header">
Chris@42 74 <p>
Chris@42 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>
Chris@42 76 </div>
Chris@42 77 <hr>
Chris@42 78 <a name="Complex-DFTs-1"></a>
Chris@42 79 <h4 class="subsection">4.3.1 Complex DFTs</h4>
Chris@42 80
Chris@42 81 <div class="example">
Chris@42 82 <pre class="example">fftw_plan fftw_plan_dft_1d(int n0,
Chris@42 83 fftw_complex *in, fftw_complex *out,
Chris@42 84 int sign, unsigned flags);
Chris@42 85 fftw_plan fftw_plan_dft_2d(int n0, int n1,
Chris@42 86 fftw_complex *in, fftw_complex *out,
Chris@42 87 int sign, unsigned flags);
Chris@42 88 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
Chris@42 89 fftw_complex *in, fftw_complex *out,
Chris@42 90 int sign, unsigned flags);
Chris@42 91 fftw_plan fftw_plan_dft(int rank, const int *n,
Chris@42 92 fftw_complex *in, fftw_complex *out,
Chris@42 93 int sign, unsigned flags);
Chris@42 94 </pre></div>
Chris@42 95 <a name="index-fftw_005fplan_005fdft_005f1d-1"></a>
Chris@42 96 <a name="index-fftw_005fplan_005fdft_005f2d-1"></a>
Chris@42 97 <a name="index-fftw_005fplan_005fdft_005f3d-1"></a>
Chris@42 98 <a name="index-fftw_005fplan_005fdft-1"></a>
Chris@42 99
Chris@42 100 <p>Plan a complex input/output discrete Fourier transform (DFT) in zero or
Chris@42 101 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@42 102 </p>
Chris@42 103 <p>Once you have created a plan for a certain transform type and
Chris@42 104 parameters, then creating another plan of the same type and parameters,
Chris@42 105 but for different arrays, is fast and shares constant data with the
Chris@42 106 first plan (if it still exists).
Chris@42 107 </p>
Chris@42 108 <p>The planner returns <code>NULL</code> if the plan cannot be created. In the
Chris@42 109 standard FFTW distribution, the basic interface is guaranteed to return
Chris@42 110 a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
Chris@42 111 using a customized FFTW configuration supporting a restricted set of
Chris@42 112 transforms.
Chris@42 113 </p>
Chris@42 114 <a name="Arguments"></a>
Chris@42 115 <h4 class="subsubheading">Arguments</h4>
Chris@42 116 <ul>
Chris@42 117 <li> <code>rank</code> is the rank of the transform (it should be the size of the
Chris@42 118 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
Chris@42 119 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
Chris@42 120 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
Chris@42 121 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
Chris@42 122 copy of one number from input to output.
Chris@42 123
Chris@42 124 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
Chris@42 125 for each routine) specify the size of the transform dimensions. They
Chris@42 126 can be any positive integer.
Chris@42 127
Chris@42 128 <ul class="no-bullet">
Chris@42 129 <li>- <a name="index-row_002dmajor-1"></a>
Chris@42 130 Multi-dimensional arrays are stored in row-major order with dimensions:
Chris@42 131 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
Chris@42 132 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
Chris@42 133 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
Chris@42 134 </li><li>- FFTW is best at handling sizes of the form
Chris@42 135 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@42 136 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
Chris@42 137 are arbitrary. Other sizes are computed by means of a slow,
Chris@42 138 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
Chris@42 139 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
Chris@42 140 Transforms whose sizes are powers of <em>2</em> are especially fast.
Chris@42 141 </li></ul>
Chris@42 142
Chris@42 143 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@42 144 transform, which may be the same (yielding an in-place transform).
Chris@42 145 <a name="index-in_002dplace-2"></a>
Chris@42 146 These arrays are overwritten during planning, unless
Chris@42 147 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@42 148 initialized, but they must be allocated.)
Chris@42 149
Chris@42 150 <p>If <code>in == out</code>, the transform is <em>in-place</em> and the input
Chris@42 151 array is overwritten. If <code>in != out</code>, the two arrays must
Chris@42 152 not overlap (but FFTW does not check for this condition).
Chris@42 153 </p>
Chris@42 154 </li><li> <a name="index-FFTW_005fFORWARD-2"></a>
Chris@42 155 <a name="index-FFTW_005fBACKWARD-2"></a>
Chris@42 156 <code>sign</code> is the sign of the exponent in the formula that defines the
Chris@42 157 Fourier transform. It can be <em>-1</em> (= <code>FFTW_FORWARD</code>) or
Chris@42 158 <em>+1</em> (= <code>FFTW_BACKWARD</code>).
Chris@42 159
Chris@42 160 </li><li> <a name="index-flags-2"></a>
Chris@42 161 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
Chris@42 162 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@42 163
Chris@42 164 </li></ul>
Chris@42 165
Chris@42 166 <p>FFTW computes an unnormalized transform: computing a forward followed by
Chris@42 167 a backward transform (or vice versa) will result in the original data
Chris@42 168 multiplied by the size of the transform (the product of the dimensions).
Chris@42 169 <a name="index-normalization-5"></a>
Chris@42 170 For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
Chris@42 171 </p>
Chris@42 172 <hr>
Chris@42 173 <div class="header">
Chris@42 174 <p>
Chris@42 175 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>
Chris@42 176 </div>
Chris@42 177
Chris@42 178
Chris@42 179
Chris@42 180 </body>
Chris@42 181 </html>