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Replace these with versions built using an older toolset (so as to avoid ABI compatibilities when linking on Ubuntu 14.04 for packaging purposes)
author Chris Cannam
date Fri, 07 Feb 2020 11:51:13 +0000
parents 37bf6b4a2645
children
rev   line source
Chris@10 1 <html lang="en">
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Chris@10 3 <title>Complex DFTs - FFTW 3.3.3</title>
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Chris@10 13 This manual is for FFTW
Chris@10 14 (version 3.3.3, 25 November 2012).
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Chris@10 16 Copyright (C) 2003 Matteo Frigo.
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Chris@10 46 </head>
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Chris@10 48 <div class="node">
Chris@10 49 <a name="Complex-DFTs"></a>
Chris@10 50 <p>
Chris@10 51 Next:&nbsp;<a rel="next" accesskey="n" href="Planner-Flags.html#Planner-Flags">Planner Flags</a>,
Chris@10 52 Previous:&nbsp;<a rel="previous" accesskey="p" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>,
Chris@10 53 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
Chris@10 54 <hr>
Chris@10 55 </div>
Chris@10 56
Chris@10 57 <h4 class="subsection">4.3.1 Complex DFTs</h4>
Chris@10 58
Chris@10 59 <pre class="example"> fftw_plan fftw_plan_dft_1d(int n0,
Chris@10 60 fftw_complex *in, fftw_complex *out,
Chris@10 61 int sign, unsigned flags);
Chris@10 62 fftw_plan fftw_plan_dft_2d(int n0, int n1,
Chris@10 63 fftw_complex *in, fftw_complex *out,
Chris@10 64 int sign, unsigned flags);
Chris@10 65 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
Chris@10 66 fftw_complex *in, fftw_complex *out,
Chris@10 67 int sign, unsigned flags);
Chris@10 68 fftw_plan fftw_plan_dft(int rank, const int *n,
Chris@10 69 fftw_complex *in, fftw_complex *out,
Chris@10 70 int sign, unsigned flags);
Chris@10 71 </pre>
Chris@10 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>
Chris@10 73 Plan a complex input/output discrete Fourier transform (DFT) in zero or
Chris@10 74 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@10 75
Chris@10 76 <p>Once you have created a plan for a certain transform type and
Chris@10 77 parameters, then creating another plan of the same type and parameters,
Chris@10 78 but for different arrays, is fast and shares constant data with the
Chris@10 79 first plan (if it still exists).
Chris@10 80
Chris@10 81 <p>The planner returns <code>NULL</code> if the plan cannot be created. In the
Chris@10 82 standard FFTW distribution, the basic interface is guaranteed to return
Chris@10 83 a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
Chris@10 84 using a customized FFTW configuration supporting a restricted set of
Chris@10 85 transforms.
Chris@10 86
Chris@10 87 <h5 class="subsubheading">Arguments</h5>
Chris@10 88
Chris@10 89 <ul>
Chris@10 90 <li><code>rank</code> is the rank of the transform (it should be the size of the
Chris@10 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
Chris@10 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
Chris@10 93 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
Chris@10 94 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
Chris@10 95 copy of one number from input to output.
Chris@10 96
Chris@10 97 <li><code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
Chris@10 98 for each routine) specify the size of the transform dimensions. They
Chris@10 99 can be any positive integer.
Chris@10 100
Chris@10 101 <ul>
Chris@10 102 <li><a name="index-row_002dmajor-165"></a>Multi-dimensional arrays are stored in row-major order with dimensions:
Chris@10 103 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
Chris@10 104 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
Chris@10 105 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
Chris@10 106 <li>FFTW is best at handling sizes of the form
Chris@10 107 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@10 108 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
Chris@10 109 are arbitrary. Other sizes are computed by means of a slow,
Chris@10 110 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
Chris@10 111 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
Chris@10 112 Transforms whose sizes are powers of 2 are especially fast.
Chris@10 113 </ul>
Chris@10 114
Chris@10 115 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@10 116 transform, which may be the same (yielding an in-place transform).
Chris@10 117 <a name="index-in_002dplace-166"></a>These arrays are overwritten during planning, unless
Chris@10 118 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@10 119 initialized, but they must be allocated.)
Chris@10 120
Chris@10 121 <p>If <code>in == out</code>, the transform is <dfn>in-place</dfn> and the input
Chris@10 122 array is overwritten. If <code>in != out</code>, the two arrays must
Chris@10 123 not overlap (but FFTW does not check for this condition).
Chris@10 124
Chris@10 125 <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
Chris@10 126 Fourier transform. It can be -1 (= <code>FFTW_FORWARD</code>) or
Chris@10 127 +1 (= <code>FFTW_BACKWARD</code>).
Chris@10 128
Chris@10 129 <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,
Chris@10 130 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@10 131
Chris@10 132 </ul>
Chris@10 133
Chris@10 134 <p>FFTW computes an unnormalized transform: computing a forward followed by
Chris@10 135 a backward transform (or vice versa) will result in the original data
Chris@10 136 multiplied by the size of the transform (the product of the dimensions).
Chris@10 137 <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>.
Chris@10 138
Chris@10 139 <!-- =========> -->
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Chris@10 141