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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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Permission is granted to make and distribute verbatim copies of this
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manual provided the copyright notice and this permission notice are
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preserved on all copies.
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Permission is granted to copy and distribute modified versions of this
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manual under the conditions for verbatim copying, provided that the
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entire resulting derived work is distributed under the terms of a
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Permission is granted to copy and distribute translations of this manual
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<head>
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<title>Real-to-Real Transform Kinds (FFTW 3.3.10)</title>
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<meta name="description" content="Real-to-Real Transform Kinds (FFTW 3.3.10)">
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="Basic-Interface.html" rel="up" title="Basic Interface">
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<link href="Advanced-Interface.html" rel="next" title="Advanced Interface">
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</head>
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<span id="Real_002dto_002dReal-Transform-Kinds"></span><div class="header">
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<p>
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Previous: <a href="Real_002dto_002dReal-Transforms.html" accesskey="p" rel="prev">Real-to-Real Transforms</a>, Up: <a href="Basic-Interface.html" 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" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<span id="Real_002dto_002dReal-Transform-Kinds-1"></span><h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4>
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<span id="index-kind-_0028r2r_0029-1"></span>
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<p>FFTW currently supports 11 different r2r transform kinds, specified by
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one of the constants below. For the precise definitions of these
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transforms, see <a href="What-FFTW-Really-Computes.html">What FFTW Really Computes</a>. For a more colloquial
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introduction to these transform kinds, see <a href="More-DFTs-of-Real-Data.html">More DFTs of Real Data</a>.
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</p>
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<p>For dimension of size <code>n</code>, there is a corresponding “logical”
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dimension <code>N</code> that determines the normalization (and the optimal
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factorization); the formula for <code>N</code> is given for each kind below.
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Also, with each transform kind is listed its corrsponding inverse
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transform. FFTW computes unnormalized transforms: a transform followed
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by its inverse will result in the original data multiplied by <code>N</code>
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(or the product of the <code>N</code>’s for each dimension, in
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multi-dimensions).
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<span id="index-normalization-7"></span>
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</p>
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<ul>
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<li> <span id="index-FFTW_005fR2HC-1"></span>
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<code>FFTW_R2HC</code> computes a real-input DFT with output in
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“halfcomplex” format, i.e. real and imaginary parts for a transform of
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size <code>n</code> stored as:
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<p align=center>
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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>
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</p>
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(Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.)
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</li><li> <span id="index-FFTW_005fHC2R-1"></span>
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<code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above.
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(Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.)
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</li><li> <span id="index-FFTW_005fDHT-1"></span>
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<code>FFTW_DHT</code> computes a discrete Hartley transform.
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(Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.)
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<span id="index-discrete-Hartley-transform-1"></span>
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</li><li> <span id="index-FFTW_005fREDFT00-2"></span>
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<code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I.
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(Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.)
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<span id="index-discrete-cosine-transform-1"></span>
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<span id="index-DCT-1"></span>
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</li><li> <span id="index-FFTW_005fREDFT10-1"></span>
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<code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called “the” DCT).
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(Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.)
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</li><li> <span id="index-FFTW_005fREDFT01-1"></span>
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<code>FFTW_REDFT01</code> computes an REDFT01 transform, i.e. a DCT-III (sometimes called “the” IDCT, being the inverse of DCT-II).
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(Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.)
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<span id="index-IDCT-2"></span>
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</li><li> <span id="index-FFTW_005fREDFT11-1"></span>
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<code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV.
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(Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.)
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</li><li> <span id="index-FFTW_005fRODFT00-1"></span>
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<code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I.
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(Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.)
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<span id="index-discrete-sine-transform-1"></span>
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<span id="index-DST-1"></span>
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</li><li> <span id="index-FFTW_005fRODFT10-1"></span>
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<code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II.
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(Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.)
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</li><li> <span id="index-FFTW_005fRODFT01-1"></span>
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<code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III.
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(Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.)
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</li><li> <span id="index-FFTW_005fRODFT11-1"></span>
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<code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV.
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(Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.)
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</li></ul>
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<hr>
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<div class="header">
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<p>
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Previous: <a href="Real_002dto_002dReal-Transforms.html" accesskey="p" rel="prev">Real-to-Real Transforms</a>, Up: <a href="Basic-Interface.html" 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" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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</html>
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