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Current fftw source
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 18 Oct 2016 13:40:26 +0100
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25 <title>FFTW 3.3.5: Real-to-Real Transform Kinds</title>
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72 <a name="Real_002dto_002dReal-Transform-Kinds"></a>
73 <div class="header">
74 <p>
75 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> &nbsp; [<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>
76 </div>
77 <hr>
78 <a name="Real_002dto_002dReal-Transform-Kinds-1"></a>
79 <h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4>
80 <a name="index-kind-_0028r2r_0029-1"></a>
81
82 <p>FFTW currently supports 11 different r2r transform kinds, specified by
83 one of the constants below. For the precise definitions of these
84 transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial
85 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>.
86 </p>
87 <p>For dimension of size <code>n</code>, there is a corresponding &ldquo;logical&rdquo;
88 dimension <code>N</code> that determines the normalization (and the optimal
89 factorization); the formula for <code>N</code> is given for each kind below.
90 Also, with each transform kind is listed its corrsponding inverse
91 transform. FFTW computes unnormalized transforms: a transform followed
92 by its inverse will result in the original data multiplied by <code>N</code>
93 (or the product of the <code>N</code>&rsquo;s for each dimension, in
94 multi-dimensions).
95 <a name="index-normalization-7"></a>
96 </p>
97 <ul>
98 <li> <a name="index-FFTW_005fR2HC-1"></a>
99 <code>FFTW_R2HC</code> computes a real-input DFT with output in
100 &ldquo;halfcomplex&rdquo; format, i.e. real and imaginary parts for a transform of
101 size <code>n</code> stored as:
102 <p align=center>
103 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>
104 </p>(Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.)
105
106 </li><li> <a name="index-FFTW_005fHC2R-1"></a>
107 <code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above.
108 (Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.)
109
110 </li><li> <a name="index-FFTW_005fDHT-1"></a>
111 <code>FFTW_DHT</code> computes a discrete Hartley transform.
112 (Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.)
113 <a name="index-discrete-Hartley-transform-1"></a>
114
115 </li><li> <a name="index-FFTW_005fREDFT00-2"></a>
116 <code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I.
117 (Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.)
118 <a name="index-discrete-cosine-transform-1"></a>
119 <a name="index-DCT-1"></a>
120
121 </li><li> <a name="index-FFTW_005fREDFT10-1"></a>
122 <code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called &ldquo;the&rdquo; DCT).
123 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.)
124
125 </li><li> <a name="index-FFTW_005fREDFT01-1"></a>
126 <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).
127 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.)
128 <a name="index-IDCT-2"></a>
129
130 </li><li> <a name="index-FFTW_005fREDFT11-1"></a>
131 <code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV.
132 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.)
133
134 </li><li> <a name="index-FFTW_005fRODFT00-1"></a>
135 <code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I.
136 (Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.)
137 <a name="index-discrete-sine-transform-1"></a>
138 <a name="index-DST-1"></a>
139
140 </li><li> <a name="index-FFTW_005fRODFT10-1"></a>
141 <code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II.
142 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.)
143
144 </li><li> <a name="index-FFTW_005fRODFT01-1"></a>
145 <code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III.
146 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.)
147
148 </li><li> <a name="index-FFTW_005fRODFT11-1"></a>
149 <code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV.
150 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.)
151
152 </li></ul>
153
154 <hr>
155 <div class="header">
156 <p>
157 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> &nbsp; [<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>
158 </div>
159
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