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author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
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3 <title>Complex DFTs - FFTW 3.3.3</title>
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13 This manual is for FFTW
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49 <a name="Complex-DFTs"></a>
50 <p>
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 n0,
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-161"></a><a name="index-fftw_005fplan_005fdft_005f2d-162"></a><a name="index-fftw_005fplan_005fdft_005f3d-163"></a><a name="index-fftw_005fplan_005fdft-164"></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. In the
82 standard FFTW distribution, the basic interface is guaranteed to return
83 a non-<code>NULL</code> plan. A plan may be <code>NULL</code>, however, if you are
84 using a customized FFTW configuration supporting a restricted set of
85 transforms.
86
87 <h5 class="subsubheading">Arguments</h5>
88
89 <ul>
90 <li><code>rank</code> is the rank of the transform (it should be the size of the
91 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
92 &lsquo;<samp><span class="samp">_1d</span></samp>&rsquo;, &lsquo;<samp><span class="samp">_2d</span></samp>&rsquo;, and &lsquo;<samp><span class="samp">_3d</span></samp>&rsquo; planners correspond to a
93 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. The rank
94 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
95 copy of one number from input to output.
96
97 <li><code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code> (as appropriate
98 for each routine) specify the size of the transform dimensions. They
99 can be any positive integer.
100
101 <ul>
102 <li><a name="index-row_002dmajor-165"></a>Multi-dimensional arrays are stored in row-major order with dimensions:
103 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
104 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
105 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
106 <li>FFTW is best at handling sizes of the form
107 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
108 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
109 are arbitrary. Other sizes are computed by means of a slow,
110 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
111 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.
112 Transforms whose sizes are powers of 2 are especially fast.
113 </ul>
114
115 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
116 transform, which may be the same (yielding an in-place transform).
117 <a name="index-in_002dplace-166"></a>These arrays are overwritten during planning, unless
118 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
119 initialized, but they must be allocated.)
120
121 <p>If <code>in == out</code>, the transform is <dfn>in-place</dfn> and the input
122 array is overwritten. If <code>in != out</code>, the two arrays must
123 not overlap (but FFTW does not check for this condition).
124
125 <li><a name="index-FFTW_005fFORWARD-167"></a><a name="index-FFTW_005fBACKWARD-168"></a><code>sign</code> is the sign of the exponent in the formula that defines the
126 Fourier transform. It can be -1 (= <code>FFTW_FORWARD</code>) or
127 +1 (= <code>FFTW_BACKWARD</code>).
128
129 <li><a name="index-flags-169"></a><code>flags</code> is a bitwise OR (&lsquo;<samp><span class="samp">|</span></samp>&rsquo;) of zero or more planner flags,
130 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
131
132 </ul>
133
134 <p>FFTW computes an unnormalized transform: computing a forward followed by
135 a backward transform (or vice versa) will result in the original data
136 multiplied by the size of the transform (the product of the dimensions).
137 <a name="index-normalization-170"></a>For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
138
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