cannam@167: <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> cannam@167: <html> cannam@167: <!-- This manual is for FFTW cannam@167: (version 3.3.8, 24 May 2018). cannam@167: cannam@167: Copyright (C) 2003 Matteo Frigo. cannam@167: cannam@167: Copyright (C) 2003 Massachusetts Institute of Technology. cannam@167: cannam@167: Permission is granted to make and distribute verbatim copies of this cannam@167: manual provided the copyright notice and this permission notice are cannam@167: preserved on all copies. cannam@167: cannam@167: Permission is granted to copy and distribute modified versions of this cannam@167: manual under the conditions for verbatim copying, provided that the cannam@167: entire resulting derived work is distributed under the terms of a cannam@167: permission notice identical to this one. cannam@167: cannam@167: Permission is granted to copy and distribute translations of this manual cannam@167: into another language, under the above conditions for modified versions, cannam@167: except that this permission notice may be stated in a translation cannam@167: approved by the Free Software Foundation. --> cannam@167: <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ --> cannam@167: <head> cannam@167: <title>FFTW 3.3.8: Real-to-Real Transform Kinds</title> cannam@167: cannam@167: <meta name="description" content="FFTW 3.3.8: Real-to-Real Transform Kinds"> cannam@167: <meta name="keywords" content="FFTW 3.3.8: Real-to-Real Transform Kinds"> cannam@167: <meta name="resource-type" content="document"> cannam@167: <meta name="distribution" content="global"> cannam@167: <meta name="Generator" content="makeinfo"> cannam@167: <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> cannam@167: <link href="index.html#Top" rel="start" title="Top"> cannam@167: <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index"> cannam@167: <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> cannam@167: <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface"> cannam@167: <link href="Advanced-Interface.html#Advanced-Interface" rel="next" title="Advanced Interface"> cannam@167: <link href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms" rel="prev" title="Real-to-Real Transforms"> cannam@167: <style type="text/css"> cannam@167: <!-- cannam@167: a.summary-letter {text-decoration: none} cannam@167: blockquote.indentedblock {margin-right: 0em} cannam@167: blockquote.smallindentedblock {margin-right: 0em; font-size: smaller} cannam@167: blockquote.smallquotation {font-size: smaller} cannam@167: div.display {margin-left: 3.2em} cannam@167: div.example {margin-left: 3.2em} cannam@167: div.lisp {margin-left: 3.2em} cannam@167: div.smalldisplay {margin-left: 3.2em} cannam@167: div.smallexample {margin-left: 3.2em} cannam@167: div.smalllisp {margin-left: 3.2em} cannam@167: kbd {font-style: oblique} cannam@167: pre.display {font-family: inherit} cannam@167: pre.format {font-family: inherit} cannam@167: pre.menu-comment {font-family: serif} cannam@167: pre.menu-preformatted {font-family: serif} cannam@167: pre.smalldisplay {font-family: inherit; font-size: smaller} cannam@167: pre.smallexample {font-size: smaller} cannam@167: pre.smallformat {font-family: inherit; font-size: smaller} cannam@167: pre.smalllisp {font-size: smaller} cannam@167: span.nolinebreak {white-space: nowrap} cannam@167: span.roman {font-family: initial; font-weight: normal} cannam@167: span.sansserif {font-family: sans-serif; font-weight: normal} cannam@167: ul.no-bullet {list-style: none} cannam@167: --> cannam@167: </style> cannam@167: cannam@167: cannam@167: </head> cannam@167: cannam@167: <body lang="en"> cannam@167: <a name="Real_002dto_002dReal-Transform-Kinds"></a> cannam@167: <div class="header"> cannam@167: <p> cannam@167: Previous: <a href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms" accesskey="p" rel="prev">Real-to-Real Transforms</a>, Up: <a href="Basic-Interface.html#Basic-Interface" 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#Concept-Index" title="Index" rel="index">Index</a>]</p> cannam@167: </div> cannam@167: <hr> cannam@167: <a name="Real_002dto_002dReal-Transform-Kinds-1"></a> cannam@167: <h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4> cannam@167: <a name="index-kind-_0028r2r_0029-1"></a> cannam@167: cannam@167: <p>FFTW currently supports 11 different r2r transform kinds, specified by cannam@167: one of the constants below. For the precise definitions of these cannam@167: transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial cannam@167: introduction to these transform kinds, see <a href="More-DFTs-of-Real-Data.html#More-DFTs-of-Real-Data">More DFTs of Real Data</a>. cannam@167: </p> cannam@167: <p>For dimension of size <code>n</code>, there is a corresponding “logical” cannam@167: dimension <code>N</code> that determines the normalization (and the optimal cannam@167: factorization); the formula for <code>N</code> is given for each kind below. cannam@167: Also, with each transform kind is listed its corrsponding inverse cannam@167: transform. FFTW computes unnormalized transforms: a transform followed cannam@167: by its inverse will result in the original data multiplied by <code>N</code> cannam@167: (or the product of the <code>N</code>’s for each dimension, in cannam@167: multi-dimensions). cannam@167: <a name="index-normalization-7"></a> cannam@167: </p> cannam@167: <ul> cannam@167: <li> <a name="index-FFTW_005fR2HC-1"></a> cannam@167: <code>FFTW_R2HC</code> computes a real-input DFT with output in cannam@167: “halfcomplex” format, i.e. real and imaginary parts for a transform of cannam@167: size <code>n</code> stored as: cannam@167: <p align=center> cannam@167: r<sub>0</sub>, r<sub>1</sub>, r<sub>2</sub>, ..., r<sub>n/2</sub>, i<sub>(n+1)/2-1</sub>, ..., i<sub>2</sub>, i<sub>1</sub> cannam@167: </p> cannam@167: (Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.) cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fHC2R-1"></a> cannam@167: <code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above. cannam@167: (Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.) cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fDHT-1"></a> cannam@167: <code>FFTW_DHT</code> computes a discrete Hartley transform. cannam@167: (Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.) cannam@167: <a name="index-discrete-Hartley-transform-1"></a> cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fREDFT00-2"></a> cannam@167: <code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I. cannam@167: (Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.) cannam@167: <a name="index-discrete-cosine-transform-1"></a> cannam@167: <a name="index-DCT-1"></a> cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fREDFT10-1"></a> cannam@167: <code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called “the” DCT). cannam@167: (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.) cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fREDFT01-1"></a> cannam@167: <code>FFTW_REDFT01</code> computes an REDFT01 transform, i.e. a DCT-III (sometimes called “the” IDCT, being the inverse of DCT-II). cannam@167: (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.) cannam@167: <a name="index-IDCT-2"></a> cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fREDFT11-1"></a> cannam@167: <code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV. cannam@167: (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.) cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fRODFT00-1"></a> cannam@167: <code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I. cannam@167: (Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.) cannam@167: <a name="index-discrete-sine-transform-1"></a> cannam@167: <a name="index-DST-1"></a> cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fRODFT10-1"></a> cannam@167: <code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II. cannam@167: (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.) cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fRODFT01-1"></a> cannam@167: <code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III. cannam@167: (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.) cannam@167: cannam@167: </li><li> <a name="index-FFTW_005fRODFT11-1"></a> cannam@167: <code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV. cannam@167: (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.) cannam@167: cannam@167: </li></ul> cannam@167: cannam@167: <hr> cannam@167: <div class="header"> cannam@167: <p> cannam@167: Previous: <a href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms" accesskey="p" rel="prev">Real-to-Real Transforms</a>, Up: <a href="Basic-Interface.html#Basic-Interface" 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#Concept-Index" title="Index" rel="index">Index</a>]</p> cannam@167: </div> cannam@167: cannam@167: cannam@167: cannam@167: </body> cannam@167: </html>