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Current fftw source
author Chris Cannam
date Tue, 18 Oct 2016 13:40:26 +0100
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3 <!-- This manual is for FFTW
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25 <title>FFTW 3.3.5: Complex DFTs</title>
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72 <a name="Complex-DFTs"></a>
73 <div class="header">
74 <p>
75 Next: <a href="Planner-Flags.html#Planner-Flags" accesskey="n" rel="next">Planner Flags</a>, Previous: <a href="Basic-Interface.html#Basic-Interface" accesskey="p" rel="prev">Basic Interface</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="Complex-DFTs-1"></a>
79 <h4 class="subsection">4.3.1 Complex DFTs</h4>
80
81 <div class="example">
82 <pre class="example">fftw_plan fftw_plan_dft_1d(int n0,
83 fftw_complex *in, fftw_complex *out,
84 int sign, unsigned flags);
85 fftw_plan fftw_plan_dft_2d(int n0, int n1,
86 fftw_complex *in, fftw_complex *out,
87 int sign, unsigned flags);
88 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
89 fftw_complex *in, fftw_complex *out,
90 int sign, unsigned flags);
91 fftw_plan fftw_plan_dft(int rank, const int *n,
92 fftw_complex *in, fftw_complex *out,
93 int sign, unsigned flags);
94 </pre></div>
95 <a name="index-fftw_005fplan_005fdft_005f1d-1"></a>
96 <a name="index-fftw_005fplan_005fdft_005f2d-1"></a>
97 <a name="index-fftw_005fplan_005fdft_005f3d-1"></a>
98 <a name="index-fftw_005fplan_005fdft-1"></a>
99
100 <p>Plan a complex input/output discrete Fourier transform (DFT) in zero or
101 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
102 </p>
103 <p>Once you have created a plan for a certain transform type and
104 parameters, then creating another plan of the same type and parameters,
105 but for different arrays, is fast and shares constant data with the
106 first plan (if it still exists).
107 </p>
108 <p>The planner returns <code>NULL</code> if the plan cannot be created. In the
109 standard FFTW distribution, the basic interface is guaranteed to return
110 a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
111 using a customized FFTW configuration supporting a restricted set of
112 transforms.
113 </p>
114 <a name="Arguments"></a>
115 <h4 class="subsubheading">Arguments</h4>
116 <ul>
117 <li> <code>rank</code> is the rank of the transform (it should be the size of the
118 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
119 &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo; planners correspond to a
120 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
121 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
122 copy of one number from input to output.
123
124 </li><li> <code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
125 for each routine) specify the size of the transform dimensions. They
126 can be any positive integer.
127
128 <ul class="no-bullet">
129 <li>- <a name="index-row_002dmajor-1"></a>
130 Multi-dimensional arrays are stored in row-major order with dimensions:
131 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
132 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
133 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
134 </li><li>- FFTW is best at handling sizes of the form
135 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
136 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
137 are arbitrary. Other sizes are computed by means of a slow,
138 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
139 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
140 Transforms whose sizes are powers of <em>2</em> are especially fast.
141 </li></ul>
142
143 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
144 transform, which may be the same (yielding an in-place transform).
145 <a name="index-in_002dplace-2"></a>
146 These arrays are overwritten during planning, unless
147 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
148 initialized, but they must be allocated.)
149
150 <p>If <code>in == out</code>, the transform is <em>in-place</em> and the input
151 array is overwritten. If <code>in != out</code>, the two arrays must
152 not overlap (but FFTW does not check for this condition).
153 </p>
154 </li><li> <a name="index-FFTW_005fFORWARD-2"></a>
155 <a name="index-FFTW_005fBACKWARD-2"></a>
156 <code>sign</code> is the sign of the exponent in the formula that defines the
157 Fourier transform. It can be <em>-1</em> (= <code>FFTW_FORWARD</code>) or
158 <em>+1</em> (= <code>FFTW_BACKWARD</code>).
159
160 </li><li> <a name="index-flags-2"></a>
161 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
162 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
163
164 </li></ul>
165
166 <p>FFTW computes an unnormalized transform: computing a forward followed by
167 a backward transform (or vice versa) will result in the original data
168 multiplied by the size of the transform (the product of the dimensions).
169 <a name="index-normalization-5"></a>
170 For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
171 </p>
172 <hr>
173 <div class="header">
174 <p>
175 Next: <a href="Planner-Flags.html#Planner-Flags" accesskey="n" rel="next">Planner Flags</a>, Previous: <a href="Basic-Interface.html#Basic-Interface" accesskey="p" rel="prev">Basic Interface</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>
176 </div>
177
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