Mercurial > hg > batch-feature-extraction-tool
diff Lib/fftw-3.2.1/doc/html/.svn/text-base/More-DFTs-of-Real-Data.html.svn-base @ 15:585caf503ef5 tip
Tidy up for ROLI
| author | Geogaddi\David <d.m.ronan@qmul.ac.uk> |
|---|---|
| date | Tue, 17 May 2016 18:50:19 +0100 |
| parents | 636c989477e7 |
| children |
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--- a/Lib/fftw-3.2.1/doc/html/.svn/text-base/More-DFTs-of-Real-Data.html.svn-base Wed May 04 11:02:59 2016 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,127 +0,0 @@ -<html lang="en"> -<head> -<title>More DFTs of Real Data - FFTW 3.2.1</title> -<meta http-equiv="Content-Type" content="text/html"> -<meta name="description" content="FFTW 3.2.1"> -<meta name="generator" content="makeinfo 4.8"> -<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 3.2.1, 5 February 2009). - -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"> -<p> -<a name="More-DFTs-of-Real-Data"></a> -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-64"></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-65"></a><a name="index-fftw_005fplan_005fr2r_005f2d-66"></a><a name="index-fftw_005fplan_005fr2r_005f3d-67"></a><a name="index-fftw_005fplan_005fr2r-68"></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_0029-69"></a><a name="index-fftw_005fr2r_005fkind-70"></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> -