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2 <head>
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3 <title>Complex DFTs - FFTW 3.2.1</title>
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4 <meta http-equiv="Content-Type" content="text/html">
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5 <meta name="description" content="FFTW 3.2.1">
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7 <link title="Top" rel="start" href="index.html#Top">
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8 <link rel="up" href="Basic-Interface.html#Basic-Interface" title="Basic Interface">
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9 <link rel="prev" href="Basic-Interface.html#Basic-Interface" title="Basic Interface">
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10 <link rel="next" href="Planner-Flags.html#Planner-Flags" title="Planner Flags">
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12 <!--
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13 This manual is for FFTW
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14 (version 3.2.1, 5 February 2009).
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15
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16 Copyright (C) 2003 Matteo Frigo.
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17
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18 Copyright (C) 2003 Massachusetts Institute of Technology.
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19
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20 Permission is granted to make and distribute verbatim copies of
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21 this manual provided the copyright notice and this permission
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22 notice are preserved on all copies.
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23
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24 Permission is granted to copy and distribute modified versions of
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25 this manual under the conditions for verbatim copying, provided
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26 that the entire resulting derived work is distributed under the
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27 terms of a permission notice identical to this one.
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28
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29 Permission is granted to copy and distribute translations of this
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30 manual into another language, under the above conditions for
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31 modified versions, except that this permission notice may be
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32 stated in a translation approved by the Free Software Foundation.
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33 -->
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45 --></style>
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46 </head>
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47 <body>
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48 <div class="node">
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49 <p>
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50 <a name="Complex-DFTs"></a>
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51 Next: <a rel="next" accesskey="n" href="Planner-Flags.html#Planner-Flags">Planner Flags</a>,
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52 Previous: <a rel="previous" accesskey="p" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>,
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53 Up: <a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
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54 <hr>
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55 </div>
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56
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57 <h4 class="subsection">4.3.1 Complex DFTs</h4>
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58
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59 <pre class="example"> fftw_plan fftw_plan_dft_1d(int n,
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60 fftw_complex *in, fftw_complex *out,
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61 int sign, unsigned flags);
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62 fftw_plan fftw_plan_dft_2d(int n0, int n1,
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63 fftw_complex *in, fftw_complex *out,
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64 int sign, unsigned flags);
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65 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
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66 fftw_complex *in, fftw_complex *out,
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67 int sign, unsigned flags);
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68 fftw_plan fftw_plan_dft(int rank, const int *n,
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69 fftw_complex *in, fftw_complex *out,
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70 int sign, unsigned flags);
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71 </pre>
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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>
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73 Plan a complex input/output discrete Fourier transform (DFT) in zero or
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74 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
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75
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76 <p>Once you have created a plan for a certain transform type and
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77 parameters, then creating another plan of the same type and parameters,
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78 but for different arrays, is fast and shares constant data with the
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79 first plan (if it still exists).
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80
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81 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
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82 non-<code>NULL</code> plan is always returned by the basic interface unless
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83 you are using a customized FFTW configuration supporting a restricted
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84 set of transforms.
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85
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86 <h5 class="subsubheading">Arguments</h5>
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87
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88 <ul>
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89 <li><code>rank</code> is the dimensionality of the transform (it should be the
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90 size of the array <code>*n</code>), and can be any non-negative integer. The
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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
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92 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. A
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93 <code>rank</code> of zero is equivalent to a transform of size 1, i.e. a copy
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94 of one number from input to output.
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95
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96 <li><code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
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97 respectively, gives the size of the transform dimensions. They can be
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98 any positive integer.
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99
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100 <ul>
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101 <li><a name="index-row_002dmajor-158"></a>Multi-dimensional arrays are stored in row-major order with dimensions:
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102 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
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103 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
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104 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
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105 <li>FFTW is best at handling sizes of the form
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106 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
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107 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
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108 are arbitrary. Other sizes are computed by means of a slow,
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109 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i> log <i>n</i>)
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110
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111 <p>performance even for prime sizes). It is possible to customize FFTW
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112 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
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113 Transforms whose sizes are powers of 2 are especially fast.
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114 </ul>
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115
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116 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
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117 transform, which may be the same (yielding an in-place transform).
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118 <a name="index-in_002dplace-159"></a>These arrays are overwritten during planning, unless
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119 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
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120 initialized, but they must be allocated.)
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121
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122 <p>If <code>in == out</code>, the transform is <dfn>in-place</dfn> and the input
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123 array is overwritten. If <code>in != out</code>, the two arrays must
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124 not overlap (but FFTW does not check for this condition).
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125
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126 <li><code>sign</code> is the sign of the exponent in the formula that defines the
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127 Fourier transform. It can be -1 (= <code>FFTW_FORWARD</code>) or
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128 +1 (= <code>FFTW_BACKWARD</code>).
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129
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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,
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131 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
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132
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133 </ul>
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134
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135 <p>FFTW computes an unnormalized transform: computing a forward followed by
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136 a backward transform (or vice versa) will result in the original data
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137 multiplied by the size of the transform (the product of the dimensions).
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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>.
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139
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140 <!-- =========> -->
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141 </body></html>
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142
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