Mercurial > hg > sv-dependency-builds
diff src/fftw-3.3.3/doc/html/Real_002ddata-DFTs.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/Real_002ddata-DFTs.html Wed Mar 20 15:35:50 2013 +0000 @@ -0,0 +1,158 @@ +<html lang="en"> +<head> +<title>Real-data DFTs - 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="Basic-Interface.html#Basic-Interface" title="Basic Interface"> +<link rel="prev" href="Planner-Flags.html#Planner-Flags" title="Planner Flags"> +<link rel="next" href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" title="Real-data DFT Array Format"> +<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="Real-data-DFTs"></a> +<a name="Real_002ddata-DFTs"></a> +<p> +Next: <a rel="next" accesskey="n" href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>, +Previous: <a rel="previous" accesskey="p" href="Planner-Flags.html#Planner-Flags">Planner Flags</a>, +Up: <a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a> +<hr> +</div> + +<h4 class="subsection">4.3.3 Real-data DFTs</h4> + +<pre class="example"> fftw_plan fftw_plan_dft_r2c_1d(int n0, + double *in, fftw_complex *out, + unsigned flags); + fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1, + double *in, fftw_complex *out, + unsigned flags); + fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2, + double *in, fftw_complex *out, + unsigned flags); + fftw_plan fftw_plan_dft_r2c(int rank, const int *n, + double *in, fftw_complex *out, + unsigned flags); +</pre> + <p><a name="index-fftw_005fplan_005fdft_005fr2c_005f1d-185"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-186"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-187"></a><a name="index-fftw_005fplan_005fdft_005fr2c-188"></a><a name="index-r2c-189"></a> +Plan a real-input/complex-output discrete Fourier transform (DFT) in +zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>). + + <p>Once you have created a plan for a certain transform type and +parameters, then creating another plan of the same type and parameters, +but for different arrays, is fast and shares constant data with the +first plan (if it still exists). + + <p>The planner returns <code>NULL</code> if the plan cannot be created. A +non-<code>NULL</code> plan is always returned by the basic interface unless +you are using a customized FFTW configuration supporting a restricted +set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag +with a multi-dimensional out-of-place c2r transform (see below). + +<h5 class="subsubheading">Arguments</h5> + + <ul> +<li><code>rank</code> is the rank of the transform (it should be the size of the +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 “rank”.) The +‘<samp><span class="samp">_1d</span></samp>’, ‘<samp><span class="samp">_2d</span></samp>’, and ‘<samp><span class="samp">_3d</span></samp>’ planners correspond to a +<code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank +may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a +copy of one real number (with zero imaginary part) from input to output. + + <li><code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate +for each routine) specify the size of the transform dimensions. They +can be any positive integer. This is different in general from the +<em>physical</em> array dimensions, which are described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>. + + <ul> +<li>FFTW is best at handling sizes of the form +2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup> + 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents +are arbitrary. Other sizes are computed by means of a slow, +general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i> log <i>n</i>) performance even for prime sizes). (It is possible to customize FFTW +for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.) +Transforms whose sizes are powers of 2 are especially fast, and +it is generally beneficial for the <em>last</em> dimension of an r2c/c2r +transform to be <em>even</em>. +</ul> + + <li><code>in</code> and <code>out</code> point to the input and output arrays of the +transform, which may be the same (yielding an in-place transform). +<a name="index-in_002dplace-190"></a>These arrays are overwritten during planning, unless +<code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be +initialized, but they must be allocated.) For an in-place transform, it +is important to remember that the real array will require padding, +described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>. +<a name="index-padding-191"></a> +<li><a name="index-flags-192"></a><code>flags</code> is a bitwise OR (‘<samp><span class="samp">|</span></samp>’) of zero or more planner flags, +as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>. + +</ul> + + <p>The inverse transforms, taking complex input (storing the non-redundant +half of a logically Hermitian array) to real output, are given by: + +<pre class="example"> fftw_plan fftw_plan_dft_c2r_1d(int n0, + fftw_complex *in, double *out, + unsigned flags); + fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1, + fftw_complex *in, double *out, + unsigned flags); + fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2, + fftw_complex *in, double *out, + unsigned flags); + fftw_plan fftw_plan_dft_c2r(int rank, const int *n, + fftw_complex *in, double *out, + unsigned flags); +</pre> + <p><a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-193"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f2d-194"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f3d-195"></a><a name="index-fftw_005fplan_005fdft_005fc2r-196"></a><a name="index-c2r-197"></a> +The arguments are the same as for the r2c transforms, except that the +input and output data formats are reversed. + + <p>FFTW computes an unnormalized transform: computing an r2c followed by a +c2r transform (or vice versa) will result in the original data +multiplied by the size of the transform (the product of the logical +dimensions). +<a name="index-normalization-198"></a>An r2c transform produces the same output as a <code>FFTW_FORWARD</code> +complex DFT of the same input, and a c2r transform is correspondingly +equivalent to <code>FFTW_BACKWARD</code>. For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. + +<!-- =========> --> + </body></html> +