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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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3 <!-- This manual is for FFTW
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6 Copyright (C) 2003 Matteo Frigo.
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25 <title>FFTW 3.3.5: Real-data DFTs</title>
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37 <link href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" rel="next" title="Real-data DFT Array Format">
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72 <a name="Real_002ddata-DFTs"></a>
73 <div class="header">
74 <p>
75 Next: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="n" rel="next">Real-data DFT Array Format</a>, Previous: <a href="Planner-Flags.html#Planner-Flags" accesskey="p" rel="prev">Planner Flags</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_002ddata-DFTs-1"></a>
79 <h4 class="subsection">4.3.3 Real-data DFTs</h4>
80
81 <div class="example">
82 <pre class="example">fftw_plan fftw_plan_dft_r2c_1d(int n0,
83 double *in, fftw_complex *out,
84 unsigned flags);
85 fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
86 double *in, fftw_complex *out,
87 unsigned flags);
88 fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
89 double *in, fftw_complex *out,
90 unsigned flags);
91 fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
92 double *in, fftw_complex *out,
93 unsigned flags);
94 </pre></div>
95 <a name="index-fftw_005fplan_005fdft_005fr2c_005f1d-1"></a>
96 <a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-1"></a>
97 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-1"></a>
98 <a name="index-fftw_005fplan_005fdft_005fr2c-1"></a>
99 <a name="index-r2c-2"></a>
100
101 <p>Plan a real-input/complex-output discrete Fourier transform (DFT) in
102 zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
103 </p>
104 <p>Once you have created a plan for a certain transform type and
105 parameters, then creating another plan of the same type and parameters,
106 but for different arrays, is fast and shares constant data with the
107 first plan (if it still exists).
108 </p>
109 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
110 non-<code>NULL</code> plan is always returned by the basic interface unless
111 you are using a customized FFTW configuration supporting a restricted
112 set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag
113 with a multi-dimensional out-of-place c2r transform (see below).
114 </p>
115 <a name="Arguments-1"></a>
116 <h4 class="subsubheading">Arguments</h4>
117 <ul>
118 <li> <code>rank</code> is the rank of the transform (it should be the size of the
119 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 &ldquo;rank&rdquo;.) The
120 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
121 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
122 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
123 copy of one real number (with zero imaginary part) from input to output.
124
125 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate
126 for each routine) specify the size of the transform dimensions. They
127 can be any positive integer. This is different in general from the
128 <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>.
129
130 <ul class="no-bullet">
131 <li>- FFTW is best at handling sizes of the form
132 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
133 11<sup>e</sup> 13<sup>f</sup>,where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
134 are arbitrary. Other sizes are computed by means of a slow,
135 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>) performance even for prime sizes). (It is possible to customize FFTW
136 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
137 Transforms whose sizes are powers of <em>2</em> are especially fast, and
138 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
139 transform to be <em>even</em>.
140 </li></ul>
141
142 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
143 transform, which may be the same (yielding an in-place transform).
144 <a name="index-in_002dplace-3"></a>
145 These arrays are overwritten during planning, unless
146 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
147 initialized, but they must be allocated.) For an in-place transform, it
148 is important to remember that the real array will require padding,
149 described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
150 <a name="index-padding-2"></a>
151
152 </li><li> <a name="index-flags-3"></a>
153 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
154 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
155
156 </li></ul>
157
158 <p>The inverse transforms, taking complex input (storing the non-redundant
159 half of a logically Hermitian array) to real output, are given by:
160 </p>
161 <div class="example">
162 <pre class="example">fftw_plan fftw_plan_dft_c2r_1d(int n0,
163 fftw_complex *in, double *out,
164 unsigned flags);
165 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
166 fftw_complex *in, double *out,
167 unsigned flags);
168 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
169 fftw_complex *in, double *out,
170 unsigned flags);
171 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
172 fftw_complex *in, double *out,
173 unsigned flags);
174 </pre></div>
175 <a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-1"></a>
176 <a name="index-fftw_005fplan_005fdft_005fc2r_005f2d"></a>
177 <a name="index-fftw_005fplan_005fdft_005fc2r_005f3d"></a>
178 <a name="index-fftw_005fplan_005fdft_005fc2r"></a>
179 <a name="index-c2r-2"></a>
180
181 <p>The arguments are the same as for the r2c transforms, except that the
182 input and output data formats are reversed.
183 </p>
184 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
185 c2r transform (or vice versa) will result in the original data
186 multiplied by the size of the transform (the product of the logical
187 dimensions).
188 <a name="index-normalization-6"></a>
189 An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
190 complex DFT of the same input, and a c2r transform is correspondingly
191 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>.
192 </p>
193 <hr>
194 <div class="header">
195 <p>
196 Next: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="n" rel="next">Real-data DFT Array Format</a>, Previous: <a href="Planner-Flags.html#Planner-Flags" accesskey="p" rel="prev">Planner Flags</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>
197 </div>
198
199
200
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202 </html>