Mercurial > hg > js-dsp-test

annotate fft/fftw/fftw-3.3.4/doc/html/Real_002dto_002dReal-Transform-Kinds.html @ 40:223f770b5341 kissfft-double tip

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Try a double-precision kissfft
author Chris Cannam
date Wed, 07 Sep 2016 10:40:32 +0100
parents 26056e866c29
children
rev   line source
Chris@19 1 <html lang="en">
Chris@19 2 <head>
Chris@19 3 <title>Real-to-Real Transform Kinds - FFTW 3.3.4</title>
Chris@19 4 <meta http-equiv="Content-Type" content="text/html">
Chris@19 5 <meta name="description" content="FFTW 3.3.4">
Chris@19 6 <meta name="generator" content="makeinfo 4.13">
Chris@19 7 <link title="Top" rel="start" href="index.html#Top">
Chris@19 8 <link rel="up" href="Basic-Interface.html#Basic-Interface" title="Basic Interface">
Chris@19 9 <link rel="prev" href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms" title="Real-to-Real Transforms">
Chris@19 10 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
Chris@19 11 <!--
Chris@19 12 This manual is for FFTW
Chris@19 13 (version 3.3.4, 20 September 2013).
Chris@19 14
Chris@19 15 Copyright (C) 2003 Matteo Frigo.
Chris@19 16
Chris@19 17 Copyright (C) 2003 Massachusetts Institute of Technology.
Chris@19 18
Chris@19 19 Permission is granted to make and distribute verbatim copies of
Chris@19 20 this manual provided the copyright notice and this permission
Chris@19 21 notice are preserved on all copies.
Chris@19 22
Chris@19 23 Permission is granted to copy and distribute modified versions of
Chris@19 24 this manual under the conditions for verbatim copying, provided
Chris@19 25 that the entire resulting derived work is distributed under the
Chris@19 26 terms of a permission notice identical to this one.
Chris@19 27
Chris@19 28 Permission is granted to copy and distribute translations of this
Chris@19 29 manual into another language, under the above conditions for
Chris@19 30 modified versions, except that this permission notice may be
Chris@19 31 stated in a translation approved by the Free Software Foundation.
Chris@19 32 -->
Chris@19 33 <meta http-equiv="Content-Style-Type" content="text/css">
Chris@19 34 <style type="text/css"><!--
Chris@19 35 pre.display { font-family:inherit }
Chris@19 36 pre.format { font-family:inherit }
Chris@19 37 pre.smalldisplay { font-family:inherit; font-size:smaller }
Chris@19 38 pre.smallformat { font-family:inherit; font-size:smaller }
Chris@19 39 pre.smallexample { font-size:smaller }
Chris@19 40 pre.smalllisp { font-size:smaller }
Chris@19 41 span.sc { font-variant:small-caps }
Chris@19 42 span.roman { font-family:serif; font-weight:normal; }
Chris@19 43 span.sansserif { font-family:sans-serif; font-weight:normal; }
Chris@19 44 --></style>
Chris@19 45 </head>
Chris@19 46 <body>
Chris@19 47 <div class="node">
Chris@19 48 <a name="Real-to-Real-Transform-Kinds"></a>
Chris@19 49 <a name="Real_002dto_002dReal-Transform-Kinds"></a>
Chris@19 50 <p>
Chris@19 51 Previous:&nbsp;<a rel="previous" accesskey="p" href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms">Real-to-Real Transforms</a>,
Chris@19 52 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
Chris@19 53 <hr>
Chris@19 54 </div>
Chris@19 55
Chris@19 56 <h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4>
Chris@19 57
Chris@19 58 <p><a name="index-kind-_0028r2r_0029-214"></a>
Chris@19 59 FFTW currently supports 11 different r2r transform kinds, specified by
Chris@19 60 one of the constants below. For the precise definitions of these
Chris@19 61 transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial
Chris@19 62 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>.
Chris@19 63
Chris@19 64 <p>For dimension of size <code>n</code>, there is a corresponding &ldquo;logical&rdquo;
Chris@19 65 dimension <code>N</code> that determines the normalization (and the optimal
Chris@19 66 factorization); the formula for <code>N</code> is given for each kind below.
Chris@19 67 Also, with each transform kind is listed its corrsponding inverse
Chris@19 68 transform. FFTW computes unnormalized transforms: a transform followed
Chris@19 69 by its inverse will result in the original data multiplied by <code>N</code>
Chris@19 70 (or the product of the <code>N</code>'s for each dimension, in
Chris@19 71 multi-dimensions).
Chris@19 72 <a name="index-normalization-215"></a>
Chris@19 73 <ul>
Chris@19 74 <li><a name="index-FFTW_005fR2HC-216"></a><code>FFTW_R2HC</code> computes a real-input DFT with output in
Chris@19 75 &ldquo;halfcomplex&rdquo; format, i.e. real and imaginary parts for a transform of
Chris@19 76 size <code>n</code> stored as:
Chris@19 77 <p align=center>
Chris@19 78 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>
Chris@19 79 </p>(Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.)
Chris@19 80
Chris@19 81 <li><a name="index-FFTW_005fHC2R-217"></a><code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above.
Chris@19 82 (Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.)
Chris@19 83
Chris@19 84 <li><a name="index-FFTW_005fDHT-218"></a><code>FFTW_DHT</code> computes a discrete Hartley transform.
Chris@19 85 (Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.)
Chris@19 86 <a name="index-discrete-Hartley-transform-219"></a>
Chris@19 87 <li><a name="index-FFTW_005fREDFT00-220"></a><code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I.
Chris@19 88 (Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.)
Chris@19 89 <a name="index-discrete-cosine-transform-221"></a><a name="index-DCT-222"></a>
Chris@19 90 <li><a name="index-FFTW_005fREDFT10-223"></a><code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called &ldquo;the&rdquo; DCT).
Chris@19 91 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.)
Chris@19 92
Chris@19 93 <li><a name="index-FFTW_005fREDFT01-224"></a><code>FFTW_REDFT01</code> computes an REDFT01 transform, i.e. a DCT-III (sometimes called &ldquo;the&rdquo; IDCT, being the inverse of DCT-II).
Chris@19 94 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.)
Chris@19 95 <a name="index-IDCT-225"></a>
Chris@19 96 <li><a name="index-FFTW_005fREDFT11-226"></a><code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV.
Chris@19 97 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.)
Chris@19 98
Chris@19 99 <li><a name="index-FFTW_005fRODFT00-227"></a><code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I.
Chris@19 100 (Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.)
Chris@19 101 <a name="index-discrete-sine-transform-228"></a><a name="index-DST-229"></a>
Chris@19 102 <li><a name="index-FFTW_005fRODFT10-230"></a><code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II.
Chris@19 103 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.)
Chris@19 104
Chris@19 105 <li><a name="index-FFTW_005fRODFT01-231"></a><code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III.
Chris@19 106 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.)
Chris@19 107
Chris@19 108 <li><a name="index-FFTW_005fRODFT11-232"></a><code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV.
Chris@19 109 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.)
Chris@19 110
Chris@19 111 </ul>
Chris@19 112
Chris@19 113 <!-- -->
Chris@19 114 </body></html>
Chris@19 115