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<html>
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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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Permission is granted to make and distribute verbatim copies of this
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manual provided the copyright notice and this permission notice are
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preserved on all copies.
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Permission is granted to copy and distribute modified versions of this
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manual under the conditions for verbatim copying, provided that the
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entire resulting derived work is distributed under the terms of a
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permission notice identical to this one.
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Permission is granted to copy and distribute translations of this manual
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except that this permission notice may be stated in a translation
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approved by the Free Software Foundation. -->
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<title>Complex DFTs (FFTW 3.3.10)</title>
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<meta name="description" content="Complex DFTs (FFTW 3.3.10)">
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="Basic-Interface.html" rel="up" title="Basic Interface">
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<link href="Planner-Flags.html" rel="next" title="Planner Flags">
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</head>
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<body lang="en">
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<span id="Complex-DFTs"></span><div class="header">
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<p>
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Next: <a href="Planner-Flags.html" accesskey="n" rel="next">Planner Flags</a>, Previous: <a href="Basic-Interface.html" accesskey="p" rel="prev">Basic Interface</a>, Up: <a href="Basic-Interface.html" accesskey="u" rel="up">Basic Interface</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<span id="Complex-DFTs-1"></span><h4 class="subsection">4.3.1 Complex DFTs</h4>
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<div class="example">
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<pre class="example">fftw_plan fftw_plan_dft_1d(int n0,
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fftw_complex *in, fftw_complex *out,
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int sign, unsigned flags);
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fftw_plan fftw_plan_dft_2d(int n0, int n1,
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fftw_complex *in, fftw_complex *out,
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int sign, unsigned flags);
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fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
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fftw_complex *in, fftw_complex *out,
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int sign, unsigned flags);
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fftw_plan fftw_plan_dft(int rank, const int *n,
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fftw_complex *in, fftw_complex *out,
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int sign, unsigned flags);
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</pre></div>
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<span id="index-fftw_005fplan_005fdft_005f1d-1"></span>
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<span id="index-fftw_005fplan_005fdft_005f2d-1"></span>
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<span id="index-fftw_005fplan_005fdft_005f3d-1"></span>
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<span id="index-fftw_005fplan_005fdft-1"></span>
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<p>Plan a complex input/output discrete Fourier transform (DFT) in zero or
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more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html">Using Plans</a>).
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</p>
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<p>Once you have created a plan for a certain transform type and
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parameters, then creating another plan of the same type and parameters,
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but for different arrays, is fast and shares constant data with the
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first plan (if it still exists).
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</p>
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<p>The planner returns <code>NULL</code> if the plan cannot be created. In the
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standard FFTW distribution, the basic interface is guaranteed to return
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a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
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using a customized FFTW configuration supporting a restricted set of
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transforms.
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</p>
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<span id="Arguments"></span><h4 class="subsubheading">Arguments</h4>
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<ul>
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<li> <code>rank</code> is the rank of the transform (it should be the size of the
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array <code>*n</code>), and can be any non-negative integer. (See <a href="Complex-Multi_002dDimensional-DFTs.html">Complex Multi-Dimensional DFTs</a>, for the definition of “rank”.) The
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‘<samp>_1d</samp>’, ‘<samp>_2d</samp>’, and ‘<samp>_3d</samp>’ planners correspond to a
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<code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
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may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
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copy of one number from input to output.
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</li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
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for each routine) specify the size of the transform dimensions. They
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can be any positive integer.
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<ul class="no-bullet">
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<li>- <span id="index-row_002dmajor-1"></span>
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Multi-dimensional arrays are stored in row-major order with dimensions:
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<code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
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<code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
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See <a href="Multi_002ddimensional-Array-Format.html">Multi-dimensional Array Format</a>.
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</li><li>- FFTW is best at handling sizes of the form
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2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
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11<sup>e</sup> 13<sup>f</sup>,
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where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
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are arbitrary. Other sizes are computed by means of a slow,
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general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i> log <i>n</i>)
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performance even for prime sizes). It is possible to customize FFTW
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for different array sizes; see <a href="Installation-and-Customization.html">Installation and Customization</a>.
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Transforms whose sizes are powers of <em>2</em> are especially fast.
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</li></ul>
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</li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
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transform, which may be the same (yielding an in-place transform).
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<span id="index-in_002dplace-2"></span>
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These arrays are overwritten during planning, unless
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<code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
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initialized, but they must be allocated.)
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<p>If <code>in == out</code>, the transform is <em>in-place</em> and the input
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array is overwritten. If <code>in != out</code>, the two arrays must
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not overlap (but FFTW does not check for this condition).
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</p>
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</li><li> <span id="index-FFTW_005fFORWARD-2"></span>
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<span id="index-FFTW_005fBACKWARD-2"></span>
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<code>sign</code> is the sign of the exponent in the formula that defines the
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Fourier transform. It can be <em>-1</em> (= <code>FFTW_FORWARD</code>) or
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<em>+1</em> (= <code>FFTW_BACKWARD</code>).
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</li><li> <span id="index-flags-2"></span>
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<code>flags</code> is a bitwise OR (‘<samp>|</samp>’) of zero or more planner flags,
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as defined in <a href="Planner-Flags.html">Planner Flags</a>.
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</li></ul>
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<p>FFTW computes an unnormalized transform: computing a forward followed by
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a backward transform (or vice versa) will result in the original data
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multiplied by the size of the transform (the product of the dimensions).
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<span id="index-normalization-5"></span>
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For more information, see <a href="What-FFTW-Really-Computes.html">What FFTW Really Computes</a>.
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</p>
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<hr>
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<div class="header">
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<p>
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Next: <a href="Planner-Flags.html" accesskey="n" rel="next">Planner Flags</a>, Previous: <a href="Basic-Interface.html" accesskey="p" rel="prev">Basic Interface</a>, Up: <a href="Basic-Interface.html" accesskey="u" rel="up">Basic Interface</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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</html>
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