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author Geogaddi\David <d.m.ronan@qmul.ac.uk>
date Thu, 09 Jul 2015 01:12:16 +0100
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1 <html lang="en">
2 <head>
3 <title>Complex DFTs - FFTW 3.2.1</title>
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16 Copyright (C) 2003 Matteo Frigo.
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49 <p>
50 <a name="Complex-DFTs"></a>
51 Next:&nbsp;<a rel="next" accesskey="n" href="Planner-Flags.html#Planner-Flags">Planner Flags</a>,
52 Previous:&nbsp;<a rel="previous" accesskey="p" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>,
53 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
54 <hr>
55 </div>
56
57 <h4 class="subsection">4.3.1 Complex DFTs</h4>
58
59 <pre class="example"> fftw_plan fftw_plan_dft_1d(int n,
60 fftw_complex *in, fftw_complex *out,
61 int sign, unsigned flags);
62 fftw_plan fftw_plan_dft_2d(int n0, int n1,
63 fftw_complex *in, fftw_complex *out,
64 int sign, unsigned flags);
65 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
66 fftw_complex *in, fftw_complex *out,
67 int sign, unsigned flags);
68 fftw_plan fftw_plan_dft(int rank, const int *n,
69 fftw_complex *in, fftw_complex *out,
70 int sign, unsigned flags);
71 </pre>
72 <p><a name="index-fftw_005fplan_005fdft_005f1d-154"></a><a name="index-fftw_005fplan_005fdft_005f2d-155"></a><a name="index-fftw_005fplan_005fdft_005f3d-156"></a><a name="index-fftw_005fplan_005fdft-157"></a>
73 Plan a complex input/output discrete Fourier transform (DFT) in zero or
74 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
75
76 <p>Once you have created a plan for a certain transform type and
77 parameters, then creating another plan of the same type and parameters,
78 but for different arrays, is fast and shares constant data with the
79 first plan (if it still exists).
80
81 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
82 non-<code>NULL</code> plan is always returned by the basic interface unless
83 you are using a customized FFTW configuration supporting a restricted
84 set of transforms.
85
86 <h5 class="subsubheading">Arguments</h5>
87
88 <ul>
89 <li><code>rank</code> is the dimensionality of the transform (it should be the
90 size of the array <code>*n</code>), and can be any non-negative integer. The
91 `<samp><span class="samp">_1d</span></samp>', `<samp><span class="samp">_2d</span></samp>', and `<samp><span class="samp">_3d</span></samp>' planners correspond to a
92 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. A
93 <code>rank</code> of zero is equivalent to a transform of size 1, i.e. a copy
94 of one number from input to output.
95
96 <li><code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
97 respectively, gives the size of the transform dimensions. They can be
98 any positive integer.
99
100 <ul>
101 <li><a name="index-row_002dmajor-158"></a>Multi-dimensional arrays are stored in row-major order with dimensions:
102 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
103 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
104 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
105 <li>FFTW is best at handling sizes of the form
106 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
107 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
108 are arbitrary. Other sizes are computed by means of a slow,
109 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
110
111 <p>performance even for prime sizes). It is possible to customize FFTW
112 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
113 Transforms whose sizes are powers of 2 are especially fast.
114 </ul>
115
116 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
117 transform, which may be the same (yielding an in-place transform).
118 <a name="index-in_002dplace-159"></a>These arrays are overwritten during planning, unless
119 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
120 initialized, but they must be allocated.)
121
122 <p>If <code>in == out</code>, the transform is <dfn>in-place</dfn> and the input
123 array is overwritten. If <code>in != out</code>, the two arrays must
124 not overlap (but FFTW does not check for this condition).
125
126 <li><code>sign</code> is the sign of the exponent in the formula that defines the
127 Fourier transform. It can be -1 (= <code>FFTW_FORWARD</code>) or
128 +1 (= <code>FFTW_BACKWARD</code>).
129
130 <li><a name="index-flags-160"></a><code>flags</code> is a bitwise OR (`<samp><span class="samp">|</span></samp>') of zero or more planner flags,
131 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
132
133 </ul>
134
135 <p>FFTW computes an unnormalized transform: computing a forward followed by
136 a backward transform (or vice versa) will result in the original data
137 multiplied by the size of the transform (the product of the dimensions).
138 <a name="index-normalization-161"></a>For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
139
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