Mercurial > hg > sv-dependency-builds
diff src/fftw-3.3.3/doc/html/More-DFTs-of-Real-Data.html @ 95:89f5e221ed7b
Add FFTW3
| author | Chris Cannam <cannam@all-day-breakfast.com> |
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| date | Wed, 20 Mar 2013 15:35:50 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.3/doc/html/More-DFTs-of-Real-Data.html Wed Mar 20 15:35:50 2013 +0000 @@ -0,0 +1,127 @@ +<html lang="en"> +<head> +<title>More DFTs of Real Data - FFTW 3.3.3</title> +<meta http-equiv="Content-Type" content="text/html"> +<meta name="description" content="FFTW 3.3.3"> +<meta name="generator" content="makeinfo 4.13"> +<link title="Top" rel="start" href="index.html#Top"> +<link rel="up" href="Tutorial.html#Tutorial" title="Tutorial"> +<link rel="prev" href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data" title="Multi-Dimensional DFTs of Real Data"> +<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> +<!-- +This manual is for FFTW +(version 3.3.3, 25 November 2012). + +Copyright (C) 2003 Matteo Frigo. + +Copyright (C) 2003 Massachusetts Institute of Technology. + + Permission is granted to make and distribute verbatim copies of + this manual provided the copyright notice and this permission + notice are preserved on all copies. + + Permission is granted to copy and distribute modified versions of + this manual under the conditions for verbatim copying, provided + that the entire resulting derived work is distributed under the + terms of a permission notice identical to this one. + + Permission is granted to copy and distribute translations of this + manual into another language, under the above conditions for + modified versions, except that this permission notice may be + stated in a translation approved by the Free Software Foundation. + --> +<meta http-equiv="Content-Style-Type" content="text/css"> +<style type="text/css"><!-- + pre.display { font-family:inherit } + pre.format { font-family:inherit } + pre.smalldisplay { font-family:inherit; font-size:smaller } + pre.smallformat { font-family:inherit; font-size:smaller } + pre.smallexample { font-size:smaller } + pre.smalllisp { font-size:smaller } + span.sc { font-variant:small-caps } + span.roman { font-family:serif; font-weight:normal; } + span.sansserif { font-family:sans-serif; font-weight:normal; } +--></style> +</head> +<body> +<div class="node"> +<a name="More-DFTs-of-Real-Data"></a> +<p> +Previous: <a rel="previous" accesskey="p" href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data">Multi-Dimensional DFTs of Real Data</a>, +Up: <a rel="up" accesskey="u" href="Tutorial.html#Tutorial">Tutorial</a> +<hr> +</div> + +<h3 class="section">2.5 More DFTs of Real Data</h3> + +<ul class="menu"> +<li><a accesskey="1" href="The-Halfcomplex_002dformat-DFT.html#The-Halfcomplex_002dformat-DFT">The Halfcomplex-format DFT</a> +<li><a accesskey="2" href="Real-even_002fodd-DFTs-_0028cosine_002fsine-transforms_0029.html#Real-even_002fodd-DFTs-_0028cosine_002fsine-transforms_0029">Real even/odd DFTs (cosine/sine transforms)</a> +<li><a accesskey="3" href="The-Discrete-Hartley-Transform.html#The-Discrete-Hartley-Transform">The Discrete Hartley Transform</a> +</ul> + +<p>FFTW supports several other transform types via a unified <dfn>r2r</dfn> +(real-to-real) interface, +<a name="index-r2r-65"></a>so called because it takes a real (<code>double</code>) array and outputs a +real array of the same size. These r2r transforms currently fall into +three categories: DFTs of real input and complex-Hermitian output in +halfcomplex format, DFTs of real input with even/odd symmetry +(a.k.a. discrete cosine/sine transforms, DCTs/DSTs), and discrete +Hartley transforms (DHTs), all described in more detail by the +following sections. + + <p>The r2r transforms follow the by now familiar interface of creating an +<code>fftw_plan</code>, executing it with <code>fftw_execute(plan)</code>, and +destroying it with <code>fftw_destroy_plan(plan)</code>. Furthermore, all +r2r transforms share the same planner interface: + +<pre class="example"> fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out, + fftw_r2r_kind kind, unsigned flags); + fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out, + fftw_r2r_kind kind0, fftw_r2r_kind kind1, + unsigned flags); + fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2, + double *in, double *out, + fftw_r2r_kind kind0, + fftw_r2r_kind kind1, + fftw_r2r_kind kind2, + unsigned flags); + fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out, + const fftw_r2r_kind *kind, unsigned flags); +</pre> + <p><a name="index-fftw_005fplan_005fr2r_005f1d-66"></a><a name="index-fftw_005fplan_005fr2r_005f2d-67"></a><a name="index-fftw_005fplan_005fr2r_005f3d-68"></a><a name="index-fftw_005fplan_005fr2r-69"></a> +Just as for the complex DFT, these plan 1d/2d/3d/multi-dimensional +transforms for contiguous arrays in row-major order, transforming (real) +input to output of the same size, where <code>n</code> specifies the +<em>physical</em> dimensions of the arrays. All positive <code>n</code> are +supported (with the exception of <code>n=1</code> for the <code>FFTW_REDFT00</code> +kind, noted in the real-even subsection below); products of small +factors are most efficient (factorizing <code>n-1</code> and <code>n+1</code> for +<code>FFTW_REDFT00</code> and <code>FFTW_RODFT00</code> kinds, described below), but +an <i>O</i>(<i>n</i> log <i>n</i>) algorithm is used even for prime sizes. + + <p>Each dimension has a <dfn>kind</dfn> parameter, of type +<code>fftw_r2r_kind</code>, specifying the kind of r2r transform to be used +for that dimension. +<a name="index-kind-_0028r2r_0029-70"></a><a name="index-fftw_005fr2r_005fkind-71"></a>(In the case of <code>fftw_plan_r2r</code>, this is an array <code>kind[rank]</code> +where <code>kind[i]</code> is the transform kind for the dimension +<code>n[i]</code>.) The kind can be one of a set of predefined constants, +defined in the following subsections. + + <p>In other words, FFTW computes the separable product of the specified +r2r transforms over each dimension, which can be used e.g. for partial +differential equations with mixed boundary conditions. (For some r2r +kinds, notably the halfcomplex DFT and the DHT, such a separable +product is somewhat problematic in more than one dimension, however, +as is described below.) + + <p>In the current version of FFTW, all r2r transforms except for the +halfcomplex type are computed via pre- or post-processing of +halfcomplex transforms, and they are therefore not as fast as they +could be. Since most other general DCT/DST codes employ a similar +algorithm, however, FFTW's implementation should provide at least +competitive performance. + +<!-- =========> --> + </body></html> +